19. Externalities

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Externalities& Common Property

Externalities

Externality:cost/beneft imposed upon someone by actions taken by others

o Cost/beneft generated externally to the someone

o Positive externality:externally provided beneft

Ex. ell!maintained property next door that raises market value o" your property

Pleasant cologne orn by the person seated next to you

#accinations against contagious diseases

$cientifc advance

o Negative externality: externality imposed cost Ex. air / ater pollution% loud parties next door% trac congestion% 'ndhand smoke

Externalities and Efciency

Externality impacts a third party

o $omeone ho is not a participant in activity that produces the external cost/beneft

o $omeone E()E*+,- to the activity

Externalities:

o ccurs henever the activities o" on economic agent aects the activities o" another agent in

ays hich are +) taken into account by operation o" market 0any activities have eects that ould +) be considered externalities

1" 1 buy a large amount o" heat in marketprice o" heat could rise 2cause

excess demand3 4 aecting activities o" other agents

0,*5E) eect price rise

Externalities and Efciency

Externalities cause Pareto ineciency4

o )oo much scarce resource allocated to an activitycauses 6ve externality

o )oo little resource is allocated to an activitycause 7ve externality

8hen externalities are harm"ul to 9rdparties -ve externalities

2ex. pollution % costs are borne by outsiderso competitive market / !ve externally "ree market produces too much o" the good

cost o" supplying good that is not borne by suppliersprivate cost used in output

decisions is too small true 0C to all agents in society includes costsborne by those externalto the

market "or the good hen externalities are benefcial to third parties +ve externalities

2ex. vaccinations% "eer carriers o" disease3o competitive market / 7ve externality "ree market produces too little o" the good

hen there is a benetto those others than primary consumers 2buyers3

0arginal $ocial :eneft ; 0arginal Private :eneft


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,pples and :ees Example

o ' "armers side by side

,F apple tree and sells apples

:F beeAkepper and sells honey

o can be done using reciprocal 7ve externalities

bees provide pollination services to ,simpli"y /G!ay 7ve externalityF

nectar "rom apple!blossoms are an input to production o" honey

, expects GA baskets o" apples "rom each tree

o total revenue depends n H o" apple trees 2linear "unction 6 more trees more apples3

o cost o" maintaining 2non!linear o" H o" trees3

o proft "unctionF

) @ H o" trees

P,@ market price o" basket o" apples

: proft depends on H o" bee!hives he keeps 7 H o" trees kept by ,

o -I1CF

0ore trees more apple blossomsmore nectarmore honey

o ProftF

: @ H o" bee!hives maintained

) @ H o" trees next!door

PJ@ price o" bee!hives production o" honey controls :% H o" bees/hives maintained

depends on H o" apple trees% not controlled by :

depends on H o" bees C+1)1+,- on H o" trees

, determines H o" trees to maintain by getting marginal beneft o" another tree 2marginal revenue

product3 ith 0C o" another treeo slope o" proft @ A

o optimal H o" trees "or , alone @ linear "or price o" apples

: determines H bee!hives to maintain by e=uating 0: ith 0C o" another bee!hive

o 0* depends on H o" trees next door

utputs aren>t socially optimal 2not pareto!optimal3

o , ignore external beneft o" apple blossoms "or honey production b/c JE J,$ + P*PE*)D

*1IJ)$ ) +EC),*o pareto!ecient determined"armers merging

change in either ill reduce proft

dierentiate combined proft .r.t K)>

and set @ A socially optimal H treesF

dierentiate .r.t K:>

optimal L "rom social perspective o" apple trees is -,*IE*

than private

Coase Theorem

possible solution to externalities


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suggestno need "or govt intervention 6 don>t need third party involvement as long as ' conditions

satisfedF

1st :

o property right must be ell!defned

ex. ho ons apples% ho ons nectar produced by apple blossoms

nd :

o no signifcant costs to transacting/bargaining

i" both conditions satisfes externality can be internali?ed through side payments (bribes)

is transaction @ costly Coase solution cant be implementedappeal to outside agency

analysis o" economics o" contract la begins ith Coase

o ex. prices o" apples% honeycan compute side payment made to compensate , "ormaintaining more trees than ould be consistent ith maximi?ing apples proft alone

Pa 2M o" basket o" apples3 @ MN

Ph 2M o" hive>s orth o" honey3 @ MGA

$ub apple M into expression "or optimal H o" trees

o )


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agent , @ endoed ith My, agent : @ endoed ith My: $moke intensity is measured on scale "rom A to G2max

concentration3

8hat are the ecient allocations o" smoke and moneyT

$uppose there is no means by hich money can be exchanged "or changes in smoke level

o 8hat is ,>s most pre"erred allocationT

o 1s this allocation ecientT

o :>s most pre"erred allocationT

o ,llocation ecientT

1" , and : cannot trade money "or changes in smoke intensityoutcome @ inecient

o Either too much smoke 2,>s most pre"erred choice3

o )oo little smoke 2:>s choice3

Externalities and Property !ights

Coase>s insight is that most externality problems are due to an inade=uate specifcation o" property

rights & an absence o" markets in hich trade can be used to internali?e externalcosts/benefts

$nternali&ing the externalityF causing producer o" externality to bear "ull external cost/ enUoy "ull

external beneft +either , nor : ons air in their room

o 8hat happens i" this property right is created and is assigned to one o" themT

$uppose : assigned onership o" air in roomcan no sell rights to smoke

8ill there be smokedT Jo muchT ,nd hat price "or this amount o" smokeT

p2s,3 @ price paid to agent , to agent : in order to create a smoke intensity o" s ,


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suppose , assigned onership o" air

o : can no pay , to reducesmoke intensity

Jo much smoking ill

there meT Jo much Mill : pay ,T

,gent given property right better o than at her on most pre"erred allocation in absence o"

property right

,mount o" smoking that occurs in e=uilibrium depends upon hich agent is assigned the property

right

'ther (tility )"nctions and Their $ndi*erence C"rves

linear in Uust x' "asi-linear

ex.

,! or ."asi-/inear (tility )"nctions

, =uasi!linear utility "unction is o" the "orm

0*$ @ !">2xG3 does not depend upon x' so the slope o" indierence

curves "or a =uasi!linear utility "unction @ constant along any line "orhich xG is constant

8hat does that make indierence map "or =uasi!linear utility "unction

look likeT

Externalities and Property !ights

is there a case in hich the same amount o" smoking occurs in

e=uilibrium no matter hich agent is assigned onership o" the air in the roomTo Des i" the 0*$ is independent o" each agents money

Ex. 1" each agent is illing to pay an identical amount o" money to 2smoke/reduce

smoking3 irrespective o that agent0s ealth

Both agents: MRS = constant as $ changes, for given smoe intensity! preferences m"st be #"asi%inear in $


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Coase0s Theorem

1" all agents> pre"erences are =uasilinear in money% then ecient level o" externality generatingcommodity is produced no matter hich agent is assigned the property right

Coase 2 Pigo"

CoaseF shoed that 1BF

o ,ll aected partied could be identifed

o Property rights ell!specifed

o :argaining is costless

)hen externality could be internali?ed through side payments

Pigo":

o ,ll aect parties cannot bet identifed

o 1" right not per"ectly specifed

o )ransacting is costly

Central rep 2govt3 can as atF

Payer o" side payments 2subsidi?e 7ve externality3

*ecipient o" side payments 2impose tax on activity causing 6ve externality3

Pigo"

Example G 6 Proposal o" Carbon )ax on C' emissions

o Carbon emissions impose costs on outsiders4 a tax per unit emitted 2,ssuming the

monitoring problem can be solved3 "orces polluters to internali?e these costs

Example ' 6 City o" 8aterloo subsidy o" rain barrels "or homeoners

o se o" ater "rom municipal system "or gardens imposes costs on al 8aterloo users

o use o" rain barrels reduces demand n ater system% can save M 2volume charge or fxed

charge through property tax3 !!! subsidy to users o" rain barrels encourages their use

Coase3 Pigo"3 and %egative Externalities

exo" negative externality

o river on the banks there are ' frms pstream & onstream

o proft o" upstream frm% as a "unction o" its activity level 2output3F

pro&tharmed by pstream frm

o e'upstream frm discharges some substance into the river ater hich must be removed%

through a costly kind o" treatment% by donstream frm be"ore the ater can be used in thedonstream frms production process

no upstreamater ould not have to be treated treatment cost borne by donstream is direct

result o" the activity o" upstream frm

donstream frms proft "unctionF

o depends on both its on activities%

hich it controls

level o" activity 2output3 o" the upstream 2donstream has no control3

optimal4prot-max#output o" (PT!E5,

o considers +-D its on production cost0* @ 0C 2slope o" proft "unction @A3

optimaloutput o" 6'7%T!E5,


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o 0* @ 0C 2slope o" proft "unction @ A3

o Ludisappears "rom dierentiation

o onstream doesn>t choose upstream frms outputcost o" cleanup is not in their control

"rpl"s-max 4pareto-efcient3 socially optimal#

o ,ssume that the ' frms merge and max a Uoint proft "unction o" ' outputs

can separate Lu% Ld

partial derivatives o" proft "unction @ derivatives o" ' component "unctionsF

o $ocially optimal level o" donstreamoutput is unchanged at 'OF

o $ocially optimal level o" "pstreamoutput "alls "rom 9A to 'AF

8JE+ 0E*IE P*B1)$ @ 0,(101VE

o pstream takes account o" ,-- costs o" production 2including donstream cost o" cleaning3

Profts maximi?ed in isolated 2not merged3o Cost considered by upstream @ private 2ignores cleanup costs3

Example external cost

o 8hen external cost is ignored upstream produces ) 0CJ output

+egative Externalities

)o seeF

o Iive property right to donstream rm

Can charge upstream frm "or using ater

onstream ons river and can sell its services "or hatever M it chooses

8hat priceT 2goal is surplus max3

0arginal private cost @ '


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5lternate 'nership

pstream ons river

onstream could pay upstream to reduce its production

0arginal 2external3 damage on donstream frm M'A/unit o" output

o onstream pay upstream license "ee that allos donstream to operate river

o Pays license "ee o" MNAA% "ee reduced by M'A "or every unit o" upstream output produced

pstream proft "unction

o *eceives revenue "rom ' sources selling output that it produces and "ee income "rom

donstream frmo Collects MNAA less M'A "or every unit or produces

pstream optimal private output0* @ 0C 2slope o" proft

"unction @ A

ptimal output again @ 'A pareto!ecient

oesn>t matter hich frm ons river

o $0E:D has property rightW not ho

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19. Externalities