Free Essay

Environmental Economics

In: Business and Management

Submitted By hedley1234yt
Words 3537
Pages 15
Externality+and+Efficiency+
Contents'
Externality+...........................................................................................................................................................+2+
Externality+and+efficiency+................................................................................................................................+2+
Consumption7consumption+externality+..........................................................................................................+3+
Marginal+benefit+and+marginal+cost+of+externality+..........................................................................................+3+
The+Coase+theorem+.........................................................................................................................................+7+
Production7production+externality+ ...............................................................................................................+12+
.
Polluting+monopolist+and+the+second+best+problem+.....................................................................................+14+
Public+goods+..................................................................................................................................................+21+
Aggregating+the+MWTP+curves+for+a+public+good+..........................................................................................+22+
Aggregated+market+demand+.........................................................................................................................+23+
Aggregating+the+MWTP+curves+for+the+public+good+......................................................................................+24+
Individual+provision+of+a+public+good+............................................................................................................+25+
Free+Rider+Problem+.......................................................................................................................................+26+

+

+

'

Externality'
+
A+ consumer’s+ or+ a+ producer’s+ activity+ affecting+ another+ person’s+ wellbeing+ without+ a+ market+ transaction+is+called+externality.+Hence+the+person+who+generated+an+externality+does+not+make+any+ payment+to+nor+receive+any+from+the+other+person+who+is+affected+by+it.+
+
Understanding+the+definition+and+the+implication+of+economic+externality+is+crucial+in+the+discussion+of+ the+main+issue+of+environmental+economics.+After+understanding+the+definition+of+externality,+we+will+ look+at+the+reason+why+the+market+allocation+is+inefficient+when+the+externality+is+present+and+discuss+ the+possible+remedies+for+the+inefficiency.++ +
Examples+of+externality:+
• A+singer+on+the+street+is+an+example+of+externality.+(If+you+like+the+singing,+we+say+that+it+is+a+ positive+externality+to+you.+Otherwise,+it+is+a+negative+externality.)+ • The+same+singer+in+a+concert+hall+charging+an+entrance+fee+is+not+an+externality.++
• Pollution+ from+ a+ factory,+ a+ beautiful+ flower+ garden,+ rude+ or+ polite+ behavior,+ an+ idea+ that+ spreads+peace+or+hate,+etc.+ +
An+example+of+a+negative+externality+(an+environmental+disaster+in+Ecuador):+
• A+ court+ in+ Ecuador's+ Amazon+ jungle+ ordered+ Chevron+ Corp.+ to+ pay+ more+ than+ $8+ billion+ in+ damages+ in+ a+ closely+ watched+ environmental+ suit.+ (LA+ Times,+ February+ 14,+ 2011,+ 3:08+ p.m.)+
The+profit+of+a+company+does+not+reflect+the+non7economic+(non7market)+cost+caused+by+the+
negative+externality+(or+pollution).++Usually+the+cost+is+born+by+somebody+else.+
+
The+goods+with+externality+are+different+from+private+goods.++Private+goods+have+no+external+effect+on+ other+ consumers+ and+ producers.+ The+ consumption+ of+ a+ private+ good+ by+ a+ consumer+ increases+ the+ utility+of+the+consumer+only.+It+does+not+increase+or+decrease+the+utility+of+other+consumers+nor+the+ production+of+other+producers.+
+
When+a+good+has+an+external+effect,+the+market+allocation+of+the+good+tends+to+be+inefficient.+We+will+ discuss+ why+ the+ market+ allocation+ is+ inefficient+ and+ how+ to+ restore+ the+ efficiency+ when+ economic+ externality+exists.+ +
Externality'and'efficiency'
+
The+ market+ allocation+ of+ resources+ is+ claimed+ to+ be+ efficient+ in+ a+ perfectly+ competitive+ world.+ The+ goods+considered+under+the+assumption+of+a+perfectly+competitive+market+are+only+the+private+goods+ that+do+not+have+external+effects.+But+there+are+goods+with+externality+in+the+real+economy.+When+the+ goods+ with+ externality+ are+ included,+ the+ market+ allocation+ usually+ becomes+ inefficient.+ The+ price+ system+fails+to+lead+the+economy+to+an+efficient+allocation+in+the+economy+with+externality.+ +
To+ give+ a+ simple+ explanation+ of+ why+ the+ price+ system+ does+ not+ work,+ let’s+ consider+ an+ example.+
Suppose+ that+ I+ decide+ the+ amount+ of+ monthly+ purchase+ of+ gas+ for+ my+ car.+ + The+ amount+ I+ consume+ depends+on+the+price.+Does+the+price+reflect+all+the+costs+that+must+be+included?+The+GHGs+emitted+ from+ my+ car+ would+ affect+ everyone+ on+ the+ Earth.+ The+ suffering+ caused+ by+ the+ pollution+ lowers+ the+

well7being+of+the+people+and+should+be+considered+as+a+cost.+But+this+cost+usually+is+not+reflected+in+ the+price+of+gas.+If+this+cost+is+included+in+the+price,+the+price+must+be+higher,+and+then+I+would+have+ driven+ less+ due+ to+ the+ increase+ in+ price.+ Hence+ the+ over+ consumption+ of+ gas+ due+ to+ the+ inaccurate+ price+signal+leads+to+inefficient+allocation.+This+example+shows+that+the+price+system+does+not+lead+the+ economy+to+an+efficient+allocation+when+there+is+externality.++
+
Hence+when+we+deal+with+goods+with+externality,+we+cannot+leave+the+economy+to+the+market+and+ expect+to+obtain+an+efficient+allocation.+The+market+should+be+restricted.+ +
We+will+look+at+two+examples+of+consumption+externality+and+production+externality+below.+And+we+
will+discuss+two+methods+of+restoring+the+efficiency:+Coase+Theorem+and+optimal+taxation.+
+
Consumption5consumption'externality'
+
Two+roommates+A+and+B+share+a+room.++A+likes+to+play+a+saxophone+and+B+does+not+like+the+music.+A’s+ and+B’s+utilities+are+the+function+of+the+amount+of+money+(M)+and+the+hours+of+Saxophone+play.+!+is+ the+maximum+hours+A+can+play.+
The+utility+functions+for+A+and+B+are:+
+
! ! = ! ! ! (! ! , ! ! )+
! ! = ! ! ! (!! , ! − ! ! )+
+
SA+is+the+hours+of+play+enjoyed+by+A.++! − ! ! +is+the+hours+of+noise+free+time+enjoyed+by+B.+
Note+that+B’s+utility+depends+on+A’s+activity+(consumption)+given+by+SA.+
!! !

The+negative+externality+implies+that+ !! ! < 0,+i.e.,(B’s+utility+decreases+as+A+plays+more+saxophone.+
+
There+are+two+possible+starting+allocations+or+designation+of+ownership.+
+
Case+ 1.+ A' has' the' ownership.' The+ allocation+ where+ A+ plays+ as+ much+ as+ she+ wants+ or+ SA+ =+!:+! =
!
!
( !! , ! , !! , 0 ).+In+this+case,+we+can+say+that+A+has+the+property+right+of+playing+music.+A+can+play+ her+ saxophone+ as+ much+ as+ she+ wants,+ which+ is+ equal+ to+!.+ And+ B+ has+ zero+ property+ right.+ Hence+ B+ owns+zero+hours+of+noise+free+time.+In+this+case,+B+may+pay+A+for+noise+free+time.+ +
Case+ 2.+ B' has' the' ownership.' The+ allocation+ where+ A+ does+ not+ play+ at+ all+ or+ SA+ =+ 0,+ then:+! =
!
!
( !! , 0 , !! , ! ).+This+is+the+opposite+case+to+case+1.+B+has+the+property+right+over+the+playing+time.+
So,+if+A+wants+to+play+the+music,+then+she+has+to+get+the+permission+from+B+or+pay+for+the+time.+
+
Marginal'benefit'and'marginal'cost'of'externality'
+
The+ marginal+ benefit+ of+ playing+ the+ saxophone+ is+ assumed+ to+ be+ decreasing+ as+ the+ playing+ time+ increases.+ Hence+ the+ marginal+ benefit+ curve+ is+ represented+ by+ a+ downward+ sloping+ curve+ as+ shown+ below.+The+marginal+cost+of+the+noise+for+B+is+increasing+as+the+hours+of+listening+to+the+music+(noise)+ increases.+The+marginal+cost+curve+is+shown+as+an+upward+sloping+curve.+

+

+

+

+
The+diagram+below+shows+the+allocation+in+case+1+where+A+can+play+as+much+as+she+wants.+

+
+
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+ A’s$MB"of"playing"the"music"
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B’s$MC"of"listening"to"the"music""

Case%1.%A%has%the%ownership.%
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the%property%right%over%the%playing.%
A%plays%until%there%is%no%marginal%ben;
efit.%"
A’s"total"benefit:"
a"+"b"+"d"

c"

B’s"total"suffering"(cost):" b"+"c"+"d" Total"benefit"–"total"cost"="a"B"c" d" S0"

Hours"of"music"

The+diagram+below+shows+the+allocation+in+case+2+where+B+has+the+property+right.+

+
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B’s$MC"of"listening"to"the"music"

A’s$MB"of"playing"the"music""

Case%2.%A%has%the%ownership.%
0#corresponds%to%case%2%where%B%has%
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B’s"total"suffering"(cost):"0"
"

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total"benefit"–"total"cost"="0"
""
b"

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Hours"of"music"

The'optimal'(efficient)'level'of'music+is+given+when+MB=MC.+In+the+diagram,+S*+is+the+efficient+alloca7 tion.+At+S*,+the+net+benefit+is+maximized+and+is+given+by+the+area+a.+ +

+
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A’s$MB"of"playing"the"music""

B’s$MC"of"listening"to"the"music""

S*%is%the%socially%optimal%%
(efficient)%solution:%
A%stops%at%S*"
A’s"total"benefit:"a"+"b"
a"

B’s"total"suffering"(cost):"b"

c"

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b"

d"

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S0"

Hours"of"music"

The'Coase'theorem'
+
There+exists+the+socially+optimal+allocation+as+shown+in+the+above+diagram.+But+achieving+the+optimal+ allocation+is+not+straight+forward+and+may+be+very+difficult.+Hence+we+may+get+stuck+at+a+non7optimal+ allocation+as+in+case+1+or+2.+
+
Coase+viewed+the+issue+of+being+stuck+at+a+non7optimal+outcome+as+the+problem+of+assigning+property+ right.+ The+ Coase+ Theorem+ said+ that+ if+ the+ property+ right+ is+ clearly+ defined,+ then+ the+ bargaining+ (or+ trade)+between+the+involved+parties+will+take+place+and+the+efficiency+will+be+obtained.+ For+example,+suppose+that+the+property+right+is+established+as+in+case+2.+Then+(

B+could+sell+the+music+time+to+A.++And+the+market+equilibrium+would+lead+to+the+optimal+allocation+S*+ as+shown+in+the+diagram+below.++ +
+
+
+

Coase'theorem:+bargaining+or+market+solution+

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A’s$MB"of"playing"the"music"

B’s$MC"of"listening"to"the"music"

a"

S*"may"be"achieved"by"bargaining" between"A"and"B,"after"the"assignment" of"ownership.""
(Privatization"works.)""
For"example,"if"B"has"the"right,"then"B" could"sell"the"music"time"to"A.""And"the" market"equilibrium"would"be"at"S*."

c"

b"

d"

S*"

S0"

Hours"of"music"

The+ Coase+ Theorem+ may+ be+ used+ to+ support+ the+ privatization+ of+ environmental+ goods+ and+ publicly+ owned+resources+and+the+allocation+through+the+market.++ +
How+ well+ does+ this+ work+ with+ environmental+ goods?+ For+ example,+ consider+ the+ allocation+ problem+ with+ clean+ air.+ The+ ownership+ of+ this+ important+ good+ is+ not+ yet+ privatized+ and+ we+ are+ facing+ major+ allocation+ problems+ with+ it.+ To+ solve+ this+ problem,+ should+ the+ air+ we+ breathe+ and+ other+ living+ organisms+depend+on+be+privatized+as+the+Coase+Theorem+suggests?+There+are+many+problems+with+ applying+the+Coase+Theorem.+We+will+discuss+a+few+of+them+below.+
+
Assigning'ownership:'
Assigning+or+distributing+property+rights+is+not+an+easy+task.+For+example,+the+Kyoto+protocol+may+be+
viewed+as+the+first+step+of+defining+property+rights.++How+much+of+the+GHGs+should+each+country+be+ allowed+ to+ emit?+ The+ international+ political+ process+ would+ determine+ the+ right+ to+ pollute+ or+ the+

ownership+of+pollution+permits.+In+a+more+serious+case,+the+ownership+of+a+piece+of+land+frequently+ has+been+decided+by+war+rather+than+by+a+peaceful+negotiation.++ +
The'cost'of'protecting'the'ownership:'
A+privatization+comes+with+the+cost+of+excluding+others+from+consuming+something.++If+enforcing+the+ right+is+too+costly,+better+leave+it+as+a+common+property.+++ For+example,+consider+a+salmon+in+a+fish+farm+vs.+a+salmon+in+the+ocean.+It+is+too+costly+to+protect+the+ ownership+ of+ a+ salmon+ in+ the+ ocean.+ This+ may+ be+ the+ reason+ why+ the+ ownership+ for+ it+ is+ not+ established.++ +
Too'many'bargaining'parties?'
A+ bargaining+ process+ may+ not+ be+ possible,+ if+ there+ are+ too+ many+ involved+ parties.+ The+ clean+ air+ is+ shared+ among+ billions+ of+ people+ including+ the+ future+ generation.+ It+ is+ impossible+ to+ assign+ the+ property+ rights.+ Even+ if+ assigning+ property+ rights+ is+ possible,+ reaching+ a+ certain+ efficient+ allocation+ through+ the+ bargaining+ (or+ trading+ through+ the+ market)+ would+ be+ impossible+ because+ there+ are+ so+ many+people+and+some+of+them+do+not+even+exist+yet.+ +
Non5market'allocation'may'be'more'efficient:+
Do+ the+ two+ roommates+ need+ to+ create+ a+ market+ by+ assigning+ the+ property+ rights?+ Usually+ we+ do+ resolve+the+issue+without+relying+on+creating+a+market.+Friends+or+people+in+a+community+not+relying+ on+a+market+may+obtain+a+more+efficient+allocation+than+through+the+market.+The+friendship+between+ the+ two+ roommates,+ the+ common+ courtesy+ or+ the+ social+ norm+ may+ be+ enough+ to+ resolve+ the+ allocation+problem+without+resorting+to+the+process+of+assigning+the+property+right+through+a+court,+ and+buying+and+selling+through+the+market+after+the+assignment.+
+
+
+
+
+
+
+

The+ social+ norm+ of+ a+ society+ other+ than+ market+ transaction+ may+ work+ well+ to+ achieve+ an+ efficient+ allocation.+For+example,+friendship+or+common+courtesy+may+be+all+we+need.+We+may+not+need+to+go+ through+an+expensive+court+process+of+assigning+property+right.+1+

+
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B’s$MC"of"listening"to"the"music""

A‘s$MB"of"playing"the"music""

a"

S*" may" be" achieved" out" of" a" common" courtesy." " A" friend" may" simply" restrict" his" playing" time" and" the" other" may" understand"his" friend" as" a" musician." (A" and"B"know"each"other"well,"(regarding" MB" and" MC)" and" a" simple" communication"between"them"may"lead" to"such"an"outcome"S*.)"

c"

b"

d"

S*"

S0"

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'

1%As"Coase"suggested,"assigning"property"right"and"creating"a"market"for"it"may"be"introduced"to"resolve"the"problem."

But"the"introduction"of"a"market"may"change"the"relationship"between"the"two"friends"as"traders,"a"buy"and"a"seller."
Their" friendship" may" be" altered" once" they" become" a" buyer" and" the" seller." Michael" Sandel" says" that" “when" market" thinking" and" values" enter" the" sphere" of" certain" social" goods" and" practices," they" change" the" meaning" of" those" practices"—"and"crowd"out"attitudes"and"norms"worth"caring"about.”"From"The"real"price"of"market"values:"Michael" Sandel" at" TEDGlobal"2013." http://blog.ted.com/2013/06/14/theBrealBpriceBofBmarketBvaluesBmichaelBsandelBatB tedglobalB2013/% Production5production'externality'
+
We+consider+two+firms,+an+upstream+firm+that+negatively+affects+the+production+of+a+downstream+firm;+
Steel+firm(S)+and+the+hotel(H).+The+steel+producer+pollutes+the+river+and+it+negatively+affects+the+hotel+
downstream.+The+negative+external+cost+on+the+hotel+is+not+included+in+the+steel+firm’s++MC.+The+social+ cost+must+include+this+external+cost.+The+MC' social+is+higher+than+the+steel+firm’s+MC+as+shown+in+the+ diagram+below.++ +
The+market+equilibrium+level+of+output+Q+is+given+at+MB=+MC'private.+The+market+equilibrium+is+not+effi7
cient.++The+socially+optimal+or+efficient+level+of+output+is+given+when+MB=+MC'social+.++The+total+surplus+ at+Q*is+given+by+the+area+“a”+and+is+bigger+than+the+total+surplus+at+Q+given+by+“a7b”+ +
+
+
+

$
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Steel+firm’s+MC'private
Q*:+(socially)+optimal+level+of+ output b a Q:+the+competitive+market+ equilibrium+level(not+efficient) •

Total+surplus+at+Q*=a
Total+surplus+at+Q=a7b

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Government'subsidy'or'tax''
To+restore+the+efficiency,+we+consider+the+introduction+of+tax+or+subsidy.+In+this+case+a+unit+tax+“t”+is+
imposed+on+steel+production.+In+the+diagram+below,+the+tax+rate+is+given+by+“t”+that+is+equal+to+the+ marginal+external+cost+of+the+steel+firm+on+the+hotel.+This+tax+internalized+the+negative+externality+ caused+by+the+steel+firm.+
After+the+introduction+of+tax,+the+steel+firm’s+marginal+cost+is+given+by+t+'MC'private.+And+the+market+

equilibrium+with+the+new+supply+curve+t+'MC'private+occurs+at+the+efficient+level+Q*+where+MB='t+'MC'
+
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Polluting'monopolist'and'the'second'best'problem'
+
Consider+a+monopolist+that+emits+pollution+while+producing+Y.+The+market+failure+here+is+due+to+two+ reasons,+monopoly+and+externality.++ +
There+are+two+opposite+effects+we+need+to+consider.+First,+a+monopolist+without+negative+externality+
produces+less+than+the+socially+optimal+level+of+output.++And+a+firm+with+negative+externality+produces+ more+ than+ the+ socially+ optimal+ level+ of+ output.+ Hence+ a+ monopolist+ with+ negative+ externality+ may+ produce+more+or+less+than+the+socially+optimal+level+of+output,+depending+on+which+effect+is+greater.++ +
+
Monopoly+with+no+externality:+When+there+is+no+externality,+the+condition+MC=MR+is+satisfied+at+the+monopo7
+
list’s+profit+maximizing+level+of+output.++
+
Q*:+Socially+optimal+output+(MC=D+or+Supply+=Demand+at+Q*.)
+
Q’:+Monopoly+profit+maximizing+level+of+output+(The+condition+MC=MR+is+satisfied+at+the+level+Q’)+
+
Note+that+the+monopolist+produces+less+than+the+socially+optimal+level.+
+
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In+this+case,+the+monopolist+produces+more+than+the+socially+optimal+level.+Again+we+have+MR=MC'private
+

at+the+monopolist’s+profit+maximizing+level+of+output,+Q’.+
+

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Given+the+two+effects,+we+may+not+be+able+to+correct+both+problems.+And+if+we+correct+just+one,+say+ the+ negative+ externality+ problem+ with+ the+ tax,+ then+ the+ expected+ outcome+ may+ not+ be+ the+ optimal+ one+ due+ to+ ignoring+ the+ other+ effect.+ In+ other+ words,+ the+ partial+ correction+ could+ be+ worse+ than+ without+any+correctional+policy.+ +
+
+

Consider+ a+ monopoly+ firm+ producing+ a+ good+ Y+ emits+ a+ certain+ pollutant.+ The+ negative+ externality+ is+ given+by+t+per+unit+of+output+Y.+In+the+diagram+below,+it+is+shown+that++ +
1. +Yc+is+the+optimal+level+of+output+if+there+is+no+pollution.+
2. Y*+is+the+optimal+(the+first+best)+level+of+output.+This+socially+optimal+level+cannot+be+achieved+ by+ correcting+ the+ externality.+ In+ other+ words,+ by+ introducing+ a+ unit+ tax+ internalizing+ the+ negative+externality+does+not+work.+In+fact,+we+need+a+subsidy+to+achieve+the+socially+optimal+ level+Y*(as+discussed+below.+
3. Y0+is+the+monopoly’s+profit+maximizing+level+of+output.++
(
Remember+that+the+monopolist+produces+the+level+of+output+at+which+the+marginal+cost+is+equal+to+ the+marginal+revenue.++I.e.,+at+Y0(+MRY+=MC.+ +
When+the+government+imposes+a+tax+t,+then+the+MC+cost+curve+shifts+to+MC(+(t.++
+
4. Yt+is+the+monopoly’s+profit+maximizing+level+of+output+after+the+tax+t+is+imposed.+
+
Note+that+after+the+introduction+of+the+tax,+the+level+of+output+decreased+from+Y0+to+Yt+and+the+total+ social+surplus+in+fact+decreased.+The+loss+is+represented+by+the+area+“abfe”.+It'is'better'not'to'correct' the'externality'by'introducing'tax.'
+
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In+this+case,+a+negative+tax+is+needed+to+obtain+the+optimal+output.+
+
Note+that+a+monopoly+in+general+produces+less+than+the+socially+optimal+level.++(1)+
But+a+firm+with+negative+externality+in+general+produces+more+than+the+socially+optimal+level.+(2)+
+
Since+(1)+dominates+(2)+in+the+case+shown,+the+monopoly’s+profit+maximizing+level+of+output+Y0+is+less+
than+socially+optimal+one.++And+the+tax+correcting+the+negative+externality+reduces+the+level+of+output+ even+further.+Hence+the+partial+correction+of+the+negative+externality+made+things+worse,+or+the+loss+ becomes+even+bigger+after+the+introduction+of+the+tax.+

The+society+should+have+provided+the+firm+with+an+incentive+to+produce+more,+i.e.,+the+negative+tax+(or+ subsidy),+to+achieve+the+optimal+level+of+output+of+Y.+ '
'

Public'goods''
+
When+a+good+is+owned+and+consumed+by+the+whole+society+it+is+called+a+public+good.+The+precise+ economic+definition+is+provided+below:++ +
• A+good+is+excludable+if+the+owner+can+exclude+others+from+consuming+the+good.+
• A+ good+ is+ a+ rival' good+ if+ one+ person’s+ consumption+ of+ the+ good+ prevents+ others+ from+ consuming+it.+ • Public'goods+are+non7rival+and+non7excludable+goods.+
• Private'goods+are+rival+and+excludable+goods.+++
'
The+following+table+shows+examples+of+goods+that+are+categorized+by+the+four+different+characteristics.++
+
+
Excludable+
Non5excludable+
Rival++
Market'Good:++
Oceanic+fisheries,+timber+
Food,+clothes,+cars,+land,+ from+unprotected++ timber,+fish+once+captured,+ forests,+air+pollution+ farmed+fish+
Non7rival+
Patented+information,+
Pure'Public'Good:''
roads+(congestible),+ defense,+climate+stability,+ozone+ streetlights,+ layer,+clean+air,+biodiversity,+ private+beaches,+private+ information,+habitat,+life+ gardens,+zoos,+movies+ support+functions,+etc.+ +
+
'

Aggregating'the'MWTP'curves'for'a'public'good'

$

+
Suppose+ good+ X+ is+ a+ public+ good+ and+ two+ people+ A+ and+ B+ are+ represented+ by+ MWTPA+ and+ MWTPB.++
Now+we+will+look+at+how+we+may+aggregate+the+two+curves.++
+
+
+
+
+
+
+
+

MWTP

MWTP

B

A

X

+

Aggregated'market'demand'

$

+
Suppose+that+X+is+a+private+good.+Then+the+market+aggregation+of+the+two+demand+curves+is+shown+in+
the+diagram+below.+The+market+demand+is+derived+by+adding+the+two+demands+horizontally.+I.e.,+for+a+ given+price+we+find+the+level+each+consumer+demands+and+add+them+up+to+find+the+market+demand+at+ that+price.+The+kinked+curve+below+shows+the+market+demand.+Adding+the+MC+curve+to+the+aggregate+ market+demand+curve+we+can+find+the+equilibrium+price+and+the+quantity.+ +
+
+
+
+
At+the+market+equilibrium+price+p*,+the+aggregate+demand,+
+ xA+xB=(X*+is+equal+to+the+aggregate+supply,(X*.+ +
+

MWTP

MWTP

Market+
Eq.+Price+
P*

MC=Market+Supply

B

Market+Demand:+

A



X
Market+
Eq.+X*

+
+

Aggregating'the'MWTP'curves'for'the'public'good+

$

+
Suppose+ that+ X+ is+ a+ public+ good.+ Then+ the+ aggregation+ of+ the+ two+ demand+ curves+ is+ shown+ in+ the+ diagram+ below.+ We+ call+ it+ the+ social+ MWTP+ curve.+ The+ SMWTP+ curve+ is+ derived+ by+ adding+ the+ two+ demands+vertically.+I.e.,+for+a+given+level+of+quantity(X,+we+find+the+level+of+MWTP+for+each+consumer+ and+add+them+up+to+find+the+SMWTP+at+that+quantity.+We+are+adding+the+two+MWTP+at+a+given+level+of+ consumption,+ because+ the+ consumption+ of+ one+ consumer+ of+ the+ public+ good+ does+ not+ diminish+ the+ other’s+consumption+of+the+good.++ +
Adding+the+MC+curve+to+the+SMWTP+we+can+find+the+efficient+allocation.+The+condition+for+an+efficient+
level+of+public+good+X+is+given+by+MWTPA+++MWTPB=MC.+
+
At+the+optimal+level+of+public+good+X*,+the+condition+MWTPA+++MWTPB=MC+is+satisfied.+
+
A
+
At+the+efficient+level+of+public+good+x*,+the+social+MWTP=MWTP +++
+
B
+
MWTP +is+equal+to+the+MC.
+
A
B
+
MWTP +++MWTP
+
+
+
+

MWTP

B

MWTP

A

B+

MWTP +++MWTP at+X*

A



+
B+

MWTP at+

X*

A+

MWTP at+

X*

X*

X

Individual'provision'of'a'public'good'
+
The+provision+of+a+public+good+by+an+individual+benefits+her+and+everyone+involved.+But+she+does+not+ take+the+external+benefit+into+consideration+when+she+makes+her+consumption+decision.+Hence+the+ cost+of+providing+the+good+is+privately+paid,+but+the+benefit+is+received+by+everyone.+This+discrepancy+ leads+to+an+inefficient+allocation+of+the+public+good.+Usually+the+individual+provision+of+a+public+good+is+ decided+at+the+level+where+the+marginal+cost+is+equal+to+her+individual+MB,+hence+the+MC+is+less+than+
the+social+MB.+Since+MC

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