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TheEconomicsofClimateChange C175
PublicGoods&Externalities
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Climatechange
as
a
market
failure
TheEconomicsofClimateChange C175
Environmentaleconomicsisforalargepartaboutmarketfailures:goods(orbads!)forwhichoneormoreoftheseassumptionsdoes
2007SternReviewontheEconomicsofClimateChange(politicalreportbySirNicholasStern(andcoauthors)toBritishgovernment):
Climatechangeisthebiggestmarketfailuretheworldhasever
seen.
GHGemissionsareduetoanexternality
w v reductionsbeinga(global)publicgood
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Publicgoods
I
TheEconomicsofClimateChange C175
Characteristicsofprivateandpublicgoods:
Excludable Nonexcludable
Rival Pureprivategood Openaccessresource
Nonrival Congestibleresource Purepublicgood
Wildernessarea
Rivalr :onea entsuseisattheex enseofanothers
Excludability:agentscanbepreventedfromusingthegood/service
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Problemswith
the
provision
of
public
goods
TheEconomicsofClimateChange C175
NonExcludability:Excludabilityisneededtopricetagagood
NonRivalry:Anadditionalconsumercanenjoythegoodatnoextracostofprovision.
Efficientequilibriumwillnolongerbewhereindividualmarginalrateofsubstitution=priceratio=marginalrateoftransformationor
marginalwillingnesstopay=price=marginalcosts
Wegetbacktothisinamoment
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Excursion:Aggregate
supply,
demand,
and
efficiency
TheEconomicsofClimateChange C175
Supplyanddemandcurvescanbeobtainedfromutilityandprofitmaximization.
Demand
corresponds
to
marginalwillingness
to
pay.
Aggregate
demand
given
byhorizontalaggregationofindividualdemandcurves. Su l corres ondstomar inalcostcurve.A re atesu l ivenb
horizontalaggregationofindividualsupplycurves.
(Net)Consumersurplus:areabetweendemandcurveandhorizontallinethroughthemarketprice.Measurefor(moneymetric)utilityofconsumers.
(Net)Producerssurplus:areabetweensupplycurveandhorizontallinethroughtheprice.Measureforprofit(revenueminuscosts)
,surplusismaximized.
Equilibriumgivenwheremarginalcostsequalmarginalbenefits
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Demandfor
private
good
TheEconomicsofClimateChange C175
AssumeaconsumeriwithwillingnesstopayVi(xi)forconsumingquantityxi
Consumerfacespricepofthegood
Utilitymaximization: maxVi
(xi
)pxi
leadsto p=Vi(xi)
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Demandfor
private
good
TheEconomicsofClimateChange C175
AssumeconsumeriwithwillingnesstopayVi(xi)forconsumingquantityxi
Consumerfacespricepatwhichonecanbuythegood
Utilitymaximization: maxVi xi pxi benefits costs
leadsto p=Vi(xi)
Remark:FormallythesettingcorrespondstoamoneymetricquasilinearutilityfunctionUi(xi,Mi)=Vi(xi)+Miwhichislinearinmoneyande.g.
concaveinxi
ThenthemarginalwillingnesstopayMWTPisthenegativeoftheMRSbetweenmoneyandgoodx
)($
iii
i
X XVX
U
MUMRSMWTP
Weknowthatinefficientequilibrium
$
i
i
M
ppp
MRS XX
y e nga sop= i xi
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Demandfor
private
good
TheEconomicsofClimateChange C175
AssumeconsumeriwithwillingnesstopayVi(xi)forconsumingquantityxi
Consumerfacespricepatwhichonecanbuythegood
Utilitymaximization: maxVi(xi)pxi
leadsto p=Vi(xi)=MWTP
Demand correspondstomarginalwillingnesstopaycurve.
IfVi xi isconcavethenbydefinitionVi xi isfalling.Example:V1 x1 =x1 100x1
Grossconsumersurplusistheareaunderthedemandcurve.Netconsumersurplus.
Aggregatedemandgivenbyhorizontalaggregationofindividualdemandcurves.
= = 1 1 1 1 2 2 2 . 2
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TheEconomicsofClimateChange C175
Supply ofprivate
goods
Wecanbreakdownprofitmaximizationinto
1. Minimizingcostsforagivenoutputbyoptimizinginputs
2. Maximizingprofitsbychoosingoptimaloutputlevel AssumeproducerjwithcostCj(xj)forsupplyingquantityxj
Producerfacespricepatwhichhecansellthegood
Profitmaximization:
maxpxjCj(xj)
p=Cj(xj)
Supplycorrespondstomarginalcostcurve. IncreasingifCj(xj)convex.
.
Example:C1(x1)=8+x12 , C2(x2)=0.5x2
2
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Supplyof
public
goods
TheEconomicsofClimateChange C175
Assumin thatthe ublic oodG is riced ever thin asbefore.
Profitmaximization:maxp j j j
leadstop=C
j
(Gj
)
Supplycorrespondstomarginalcostcurve.
Aggregatesupplygivenbyhorizontalaggregationofindividualsupplycurves.
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Demandfor
public
good
TheEconomicsofClimateChange C175
AssumeconsumeriwithwillingnesstopayVi(G)forconsumingquantityG
NotethatGnolon ercarriesanindex.Ever consumerconsumesalloftheGasthegoodisnonrival
Consumerfacespricepatwhichonecanbuythegood
ymax m za on:maxVi(G)pG
leadstop=Vi(G)
Individualdemandcorrespondsagaintomarginalwillingnesstopaycurve.
Socialdemandgivenbyverticalaggregationofindividualdemandcurves, .
Example:V1(G)=G(1000.5G) V2(G)=2G(1000.5G)
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Optimalprovision
of
public
good
TheEconomicsofClimateChange C175
Aggregatemarginalwillingnesstopayshouldequalmarginalcostsofprovidingthepublicgood:
forallproducersj. TheproducedquantitiesG sumtothetotalamountof
)((G)Vi
i jj GC
publicgoodprovidedG: GGj
j
Ormoregeneralforthemarginalrateofsubstitutionbetweenprivateandpublicgoodsishastohold
withgoodprivate
MRS _
MRTMRSi
Thisrelationisknownasthe
Samuelsoncondition
_i
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Optimalprovision ofpublicgoodsTheEconomicsofClimateChange C175
MRSA +MRSB =MWTPA +MWTPB
MC=MRT
=MWTPB
MRSA
=MWTPA
XX*
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PublicgoodsIITheEconomicsofClimateChange C175
Withprivategood,eachindividualconsumesdifferentamount,butpayssameprice:equalmarginalvaluationbyeachindividual.
Withpublic
good,
each
individual
has
toconsume
sameamount,
but
marginalvaluationcandiffer:onlythesumofthemarginalvaluationshastoe ualthemar inalcost.
Publicgoodsarenonexcludable,sonolinkbetweenpaymentand
provision:public
goods
cannot
be
provided
bythe
market.
Governmentcanprovi epu icgoo an inanceitviataxes.Forefficientamountofpublicgooditneedstoknowmarginalwillingnesstopayforallindividuals.However
Nonexcludability givesconsumersincentiveto reerideandtounderstatetheirwillingnesstopay!
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Lindahl markets
TheEconomicsofClimateChange C175
AssumethatanindividualmarketcanbeintroducedforeachconsumerofapublicgoodG
ThenthereareNconsumers,eachconsuminggoodGi,i=1,N atpricepG
i,i=1,N
DenotetheaggregatesupplyofthepublicgoodbyGanditspricebypG
ALindahl equilibriumasanallocationofgoods(includingG,Gi,i=1,N)andasetofprices(includingpGi,i=1,Nandaprice)suchthat
allfirmsmaximizetheirprofits,
allindividualsmaximizetheirutility(giventhebudgetconstraint),
allmarketsclearandforthepublicgooditholdsG=Giforall i=1,,N forthepriceofthepublicgoodholds:pG =ip
Gi .
Then(undersomeconditions)aLindahl equilibriumisParetoefficient
PrettymuchsaysthesamethingasourpictureandtheSamuelsonrule.
BecauseofnonexcludabilityandthedifficultiesofpricediscriminationLindahlmarketsgenerallystayatheoreticconstruct
Note:Excludabilitycanbenecessaryforanefficientmarketoutcome,eventhoughintheefficientmarketoutcome,in eneral,nobod willbeexcludedfromconsumin anonrivalgood!
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ExternalitiesIITheEconomicsofClimateChange C175
x erna y c ass ca on ere nega ve ex erna es
Arising in Affecting Utility/production function
onsumpt on onsumpt on , ,
Consumption Production X(K,L,YA)
+ +
++
Production Consumption UA(XA,YA,X)
Production Production Y(K,L,X)
+ +
+ +
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ExternalitiesIIITheEconomicsofClimateChange C175
Beneficial (positive) and harmful (negative) externalities
Effect on Originating in Originating in
others consumption production
infectious decease due to proximity to apiary
Adverse Noise pollution from Chemical factory discharge
water systems
GHG emissions can be in all 4 quadrants!!
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TheEconomicsofClimateChange C175
Exampleofanexternality: Productiononconsumption
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Exampleofanexternality:ProductiononproductionTheEconomicsofClimateChange C175
TwoproducersofgoodsXandY,withcosts2 2
,
E.g.twostylizedCalifornianfarms:awindmillfarmandawinery
100
XCX XXYCY
100
,
a ypeo ex erna y owe ace ere
LetpricesbepX=2andpY=3
X= x=
Y= Y= IsthataParetooptimum,i.e.efficient?
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Exampleofanexternality:Production,InefficiencyTheEconomicsofClimateChange C175
TwoproducersofgoodsXandY,withcosts2 2
,
LetpricesbepX=2andpY=3.100
XCX XXYCY
100
,
TryincreasingthenumberofwindmillsbyX=10
= =x
Y=150 Y=
Y=150?
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Exampleofanexternality:Production,InefficiencyTheEconomicsofClimateChange C175
TwoproducersofgoodsXandY,withcosts2 2
,
LetpricesbepX=2andpY=3.100
XCX XXYCY
100
,
OnlyifwecompensateproducerX,thewindmillfarmer!
amountofwine)fortheadditional10windmills
Mightsuchbargainingactuallytakeplace?
WillitleadtoParetooptimality? Whataretheobstacles?
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ExternalitiesandPublicGoodsTheEconomicsofClimateChange C175
Anexternalityinvolvesagoodorbadwhoselevelenterstheutilityorproductionfunctionofseveralpeople/firms.
Thatimplieseffectivelyadegreeofnonrivalryandnonexcludability.
aspublicbads (goods)andviceversa
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ClimateChangeandGHGsTheEconomicsofClimateChange C175
SowhatdoesthetheoryonpublicgoodsandexternalitiestellusaboutGHGemissions?
GHGsareapublicbad,mitigationisapublicgood.Thus
AcompetitivemarketequilibriumalonewillnotyieldaParetoo timal(efficient)allocation>Inprinciplewecanmakesomeindividualsbetterofwithoutmakinganyoneworseof
wanttofreeride
Becauseofnonrivalrythemarginalcostofmitigation(costoflast
mitigation(includingthebenefitsofavoidingclimatechangeimpactsinallcountries,industriesandforallindividuals)
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ClimateChangeandGHGsTheEconomicsofClimateChange C175
AnotherwaytothinkaboutGHGemissions:
GHGemissionscausenegativeexternalitiesinproductionaswellasdirectlyonwelfare
Theseexternalitiesaffecteveryonearoundtheglobeandinparticularalsoindividualsnot etalive
HOW CANWE CORRECT FOR EXTERNALITIESAND PROVIDEPUBLIC GOODSATAN OPTIMAL LEVEL?
WHAT DIFFICULTIES DOWE FACE DEPENDING ON THECHOICE OF OUR INSTRUMENT(policymeasure)?
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