ch 32 externalities
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![Page 1: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/1.jpg)
Chapter Thirty-Two
Externalities
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Externalities• An externality is a cost or a benefit imposed
upon someone by actions taken by others. The cost or benefit is thus generated externally to that somebody.
• An externally imposed benefit is a positive externality.
• An externally imposed cost is a negative externality.
![Page 3: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/3.jpg)
Examples of Negative Externalities• Air pollution.• Water pollution.• Loud parties next door.• Traffic congestion.• Second-hand cigarette smoke.• Increased insurance premiums due to
alcohol or tobacco consumption.
![Page 4: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/4.jpg)
Examples of Positive Externalities• A well-maintained property next door that
raises the market value of your property.• A pleasant cologne or scent worn by the
person seated next to you.• Improved driving habits that reduce
accident risks.• A scientific advance.
![Page 5: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/5.jpg)
Externalities and Efficiency
• Crucially, an externality impacts a third party; i.e. somebody who is not a participant in the activity that produces the external cost or benefit.
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Externalities and Efficiency• Externalities cause Pareto inefficiency;
typically– too much scarce resource is allocated to an
activity which causes a negative externality– too little resource is allocated to an activity
which causes a positive externality.
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Externalities and Property Rights• An externality will viewed as a purely public
commodity.• A commodity is purely public if– it is consumed by everyone (nonexcludability),
and– everybody consumes the entire amount of the
commodity (nonrivalry in consumption). • E.g. a broadcast television program.
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Inefficiency & Negative Externalities
• Consider two agents, A and B, and two commodities, money and smoke.
• Both smoke and money are goods for Agent A.• Money is a good and smoke is a bad for Agent
B.• Smoke is a purely public commodity.
![Page 9: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/9.jpg)
Inefficiency & Negative Externalities
• Agent A is endowed with $yA.
• Agent B is endowed with $yB.• Smoke intensity is measured on a scale from 0
(no smoke) to 1 (maximum concentration).
![Page 10: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/10.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mAyA
Money and smoke areboth goods for Agent A.
![Page 11: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/11.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mAyA
Money and smoke areboth goods for Agent A.
Better
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Inefficiency & Negative Externalities
OB
1
0
Smoke
mByB
Money is a good and smokeis a bad for Agent B.
Bette
r
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Inefficiency & Negative Externalities
OB
1
0
Smoke
mB yB
Money is a good and smokeis a bad for Agent B.
Better
![Page 14: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/14.jpg)
Inefficiency & Negative Externalities
• What are the efficient allocations of smoke and money?
![Page 15: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/15.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mAyA OB
1
0
Smoke
mB yB
![Page 16: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/16.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
![Page 17: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/17.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
![Page 18: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/18.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
![Page 19: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/19.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
Efficientallocations
![Page 20: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/20.jpg)
Inefficiency & Negative Externalities
• Suppose there is no means by which money can be exchanged for changes in smoke level.
• What then is Agent A’s most preferred allocation?
• Is this allocation efficient?
![Page 21: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/21.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
Efficientallocations
![Page 22: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/22.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
Efficientallocations
A’s choices
![Page 23: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/23.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
Efficientallocations
A’s mostpreferred choiceis inefficient
![Page 24: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/24.jpg)
Inefficiency & Negative Externalities
• Continue to suppose there is no means by which money can be exchanged for changes in smoke level.
• What is Agent B’s most preferred allocation?• Is this allocation efficient?
![Page 25: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/25.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
Efficientallocations
B’s choices
![Page 26: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/26.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
Efficientallocations
B’s mostpreferred choice
![Page 27: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/27.jpg)
Inefficiency & Negative Externalities
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
Efficientallocations
B’s mostpreferred choiceis inefficient
![Page 28: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/28.jpg)
Inefficiency & Negative Externalities
• So if A and B cannot trade money for changes in smoke intensity, then the outcome is inefficient.
• Either there is too much smoke (A’s most preferred choice) or there is too little smoke (B’s choice).
![Page 29: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/29.jpg)
Externalities and Property Rights
• Ronald Coase’s insight is that most externality problems are due to an inadequate specification of property rights and, consequently, an absence of markets in which trade can be used to internalize external costs or benefits.
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Externalities and Property Rights
• Causing a producer of an externality to bear the full external cost or to enjoy the full external benefit is called internalizing the externality.
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Externalities and Property Rights
• Neither Agent A nor Agent B owns the air in their room.
• What happens if this property right is created and is assigned to one of them?
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Externalities and Property Rights
• Suppose Agent B is assigned ownership of the air in the room.
• Agent B can now sell “rights to smoke”.• Will there be any smoking?• If so, how much smoking and what will be the
price for this amount of smoke?
![Page 33: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/33.jpg)
Externalities and Property Rights
• Let p(sA) be the price paid by Agent A to Agent B in order to create a smoke intensity of sA.
![Page 34: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/34.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
![Page 35: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/35.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
![Page 36: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/36.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
p(sA)
sA
![Page 37: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/37.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
p(sA)
Both agentsgain andthere is apositiveamount ofsmoking.
sA
![Page 38: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/38.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
p(sA)
sA
Establishinga market fortrading rightsto smoke causes an efficientallocation tobe achieved.
![Page 39: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/39.jpg)
Externalities and Property Rights
• Suppose instead that Agent A is assigned the ownership of the air in the room.
• Agent B can now pay Agent A to reduce the smoke intensity.
• How much smoking will there be?• How much money will Agent B pay to Agent
A?
![Page 40: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/40.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
![Page 41: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/41.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
![Page 42: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/42.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
sB
p(sB)
![Page 43: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/43.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
p(sB)
Both agentsgain andthere is areducedamount ofsmoking.
sB
![Page 44: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/44.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
p(sB)Establishinga market fortrading rightsto reducesmoke causes an efficientallocation tobe achieved.
sB
![Page 45: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/45.jpg)
Externalities and Property Rights• Notice that the– agent given the property right (asset) is better
off than at her own most preferred allocation in the absence of the property right.
– amount of smoking that occurs in equilibrium depends upon which agent is assigned the property right.
![Page 46: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/46.jpg)
Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
p(sB)p(sA)
sA sB
sB
sA
![Page 47: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/47.jpg)
Externalities and Property Rights
• Is there a case in which the same amount of smoking occurs in equilibrium no matter which agent is assigned ownership of the air in the room?
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Externalities and Property Rights
OA
1
0
Smoke
mA
OB
1
0
Smoke
mB
yA yB
p(sB)p(sA)
sA = sB
![Page 49: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/49.jpg)
Externalities and Property Rights
OA
1
0
Smoke
OB
1
0
Smoke
yA yB
p(sB)p(sA)
sA = sB
For both agents, the MRS is constant asmoney changes, for given smoke intensity.
![Page 50: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/50.jpg)
Externalities and Property Rights
OA
1
0
Smoke
OB
1
0
Smoke
yA yB
p(sB)p(sA)
sA = sB
So, for both agents, preferences must bequasilinear in money; U(m,s) = m + f(s).
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Coase’s Theorem
• Coase’s Theorem is: If all agents’ preferences are quasilinear in money, then the efficient level of the externality generating commodity is produced no matter which agent is assigned the property right.
![Page 52: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/52.jpg)
Production Externalities
• A steel mill produces jointly steel and pollution.
• The pollution adversely affects a nearby fishery.
• Both firms are price-takers.• pS is the market price of steel.
• pF is the market price of fish.
![Page 53: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/53.jpg)
Production Externalities
• cS(s,x) is the steel firm’s cost of producing s units of steel jointly with x units of pollution.
• If the steel firm does not face any of the external costs of its pollution production then its profit function is
• and the firm’s problem is to
s s ss x p s c s x( , ) ( , )
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Production Externalitiesmax ( , ) ( , ).,s x
s s ss x p s c s x
The first-order profit-maximizationconditions are
![Page 55: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/55.jpg)
Production Externalities
max ( , ) ( , ).,s x
s s ss x p s c s x
The first-order profit-maximizationconditions are
p c s xss
s
( , )
0
c s xx
s ( , ) .and
![Page 56: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/56.jpg)
Production Externalitiesp c s x
sss
( , )
states that the steel firm
should produce the output level of steelfor which price = marginal production cost.
![Page 57: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/57.jpg)
Production Externalitiesp c s x
sss
( , )
states that the steel firm
should produce the output level of steelfor which price = marginal production cost.
c s xx
s ( , ) is the rate at which the firm’s
internal production cost goes down as thepollution level rises
![Page 58: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/58.jpg)
Production Externalitiesp c s x
sss
( , )
states that the steel firm
should produce the output level of steelfor which price = marginal production cost.
c s xx
s ( , ) is the rate at which the firm’s
internal production cost goes down as thepollution level rises, so
c s xx
s ( , ) is the marginal cost to thefirm of pollution reduction.
![Page 59: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/59.jpg)
Production Externalities
c s xx
s ( , ) is the marginal cost to thefirm of pollution reduction.
What is the marginal benefit to the steelfirm from reducing pollution?
![Page 60: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/60.jpg)
Production Externalities
c s xx
s ( , ) is the marginal cost to thefirm of pollution reduction.
What is the marginal benefit to the steelfirm from reducing pollution?Zero, since the firm does not face itsexternal cost.Hence the steel firm chooses the pollutionlevel for which
c s xx
s ( , ) .0
![Page 61: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/61.jpg)
Production Externalities
s s x s s x( , ) ( ) 12 42 2
and the first-order profit-maximizationconditions are
12 2 s 0 2 4 ( ).xand
E.g. suppose cS(s,x) = s2 + (x - 4)2 andpS = 12. Then
![Page 62: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/62.jpg)
Production Externalitiesp ss 12 2 , determines the profit-max.
output level of steel; s* = 6.
![Page 63: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/63.jpg)
Production Externalitiesp ss 12 2 , determines the profit-max.
output level of steel; s* = 6. 2 4( )x is the marginal cost to the firm
from pollution reduction. Since it getsno benefit from this it sets x* = 4.
![Page 64: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/64.jpg)
Production Externalitiesp ss 12 2 , determines the profit-max.
output level of steel; s* = 6. 2 4( )x is the marginal cost to the firm
from pollution reduction. Since it getsno benefit from this it sets x* = 4.
s s x s s x( *, *) * * ( * )( )
$36.
12 412 6 6 4 4
2 2
2 2
The steel firm’s maximum profit level isthus
![Page 65: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/65.jpg)
Production Externalities
• The cost to the fishery of catching f units of fish when the steel mill emits x units of pollution is cF(f,x). Given f, cF(f,x) increases with x; i.e. the steel firm inflicts a negative externality on the fishery.
![Page 66: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/66.jpg)
Production Externalities
• The cost to the fishery of catching f units of fish when the steel mill emits x units of pollution is cF(f,x). Given f, cF(f,x) increases with x; i.e. the steel firm inflicts a negative externality on the fishery.
• The fishery’s profit function is
so the fishery’s problem is toF F Ff x p f c f x( ; ) ( ; )
![Page 67: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/67.jpg)
Production Externalitiesmax ( ; ) ( ; ).f
F F Ff x p f c f x
The first-order profit-maximizationcondition is
![Page 68: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/68.jpg)
Production Externalitiesmax ( ; ) ( ; ).f
F F Ff x p f c f x
The first-order profit-maximizationcondition is p c f x
fFF
( ; ) .
![Page 69: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/69.jpg)
Production Externalitiesmax ( ; ) ( ; ).f
F F Ff x p f c f x
The first-order profit-maximizationcondition is p c f x
fFF
( ; ) .
Higher pollution raises the fishery’smarginal production cost and lowers bothits output level and its profit. This is theexternal cost of the pollution.
![Page 70: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/70.jpg)
Production ExternalitiesE.g. suppose cF(f;x) = f2 + xf and pF = 10.The external cost inflicted on the fisheryby the steel firm is xf. Since the fisheryhas no control over x it must take the steelfirm’s choice of x as a given. The fishery’sprofit function is thus
F f x f f xf( ; ) 10 2
![Page 71: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/71.jpg)
Production Externalities
Given x, the first-order profit-maximizationcondition is
F f x f f xf( ; ) 10 2
10 2 f x.
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Production Externalities
Given x, the first-order profit-maximizationcondition isSo, given a pollution level x inflicted uponit, the fishery’s profit-maximizing outputlevel is f x* . 5
2
F f x f f xf( ; ) 10 2
10 2 f x.
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Production Externalities
Given x, the first-order profit-maximizationcondition isSo, given a pollution level x inflicted uponit, the fishery’s profit-maximizing outputlevel is
F f x f f xf( ; ) 10 2
Notice that the fishery produces less, andearns less profit, as the steel firm’spollution level increases.
f x* . 52
10 2 f x.
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Production Externalities The steel firm, ignoring its external cost inflicted upon the fishery,chooses x* = 4, so the fishery’sprofit-maximizing output level given thesteel firm’s choice of pollution level isf* = 3, giving the fishery a maximumprofit level of
.9$343310*xf*f*f10)x*;f(
2
2F
Notice that the external cost is $12.
f x* . 52
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Production Externalities
• Are these choices by the two firms efficient?• When the steel firm ignores the external costs
of its choices, the sum of the two firm’s profits is $36 + $9 = $45.
• Is $45 the largest possible total profit that can be achieved?
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Merger and Internalization
• Suppose the two firms merge to become one. What is the highest profit this new firm can achieve?
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Merger and Internalization
• Suppose the two firms merge to become one. What is the highest profit this new firm can achieve?
• What choices of s, f and x maximize the new firm’s profit?
m s f x s f s x f xf( , , ) ( ) . 12 10 42 2 2
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Merger and Internalizationm s f x s f s x f xf( , , ) ( ) . 12 10 42 2 2
The first-order profit-maximizationconditions are
m
m
m
ss
ff x
xx f
12 2 0
10 2 0
2 4 0
.
( ) .
The solution iss
f
x
m
m
m
6
4
2.
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Merger and Internalization
m m m m
m m m m m m m
s f x
s f s x f x f
( , , )
( )( )
$48.
12 10 412 6 10 4 6 2 4 4 2 4
2 2 2
2 2 2
And the merged firm’s maximum profitlevel is
This exceeds $45, the sum of the non-merged firms.
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Merger and Internalization• Merger has improved efficiency.• On its own, the steel firm produced x* = 4
units of pollution.• Within the merged firm, pollution production
is only xm = 2 units.• So merger has caused both an improvement
in efficiency and less pollution production. Why?
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Merger and Internalization
s s x s s x( , ) ( ) 12 42 2The steel firm’s profit function is
so the marginal cost of producing x unitsof pollution is MC x xs ( ) ( ) 2 4When it does not have to face theexternal costs of its pollution, the steelfirm increases pollution until this marginalcost is zero; hence x* = 4.
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Merger and InternalizationIn the merged firm the profit function is
m s f x s f s x f xf( , , ) ( ) . 12 10 42 2 2
The marginal cost of pollution is thusMC x fm x( ) ( ) 2 4
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Merger and InternalizationIn the merged firm the profit function is
m s f x s f s x f xf( , , ) ( ) . 12 10 42 2 2
The marginal cost of pollution isMC x fm x( ) ( ) 2 4 2 4( ) ( ).x MC xs
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Merger and InternalizationIn the merged firm the profit function is
m s f x s f s x f xf( , , ) ( ) . 12 10 42 2 2
The marginal cost of pollution isMC x fm x( ) ( ) 2 4 2 4( ) ( ).x MC xsThe merged firm’s marginal pollution costis larger because it faces the full cost ofits own pollution through increased costsof production in the fishery, so lesspollution is produced by the merged firm.
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Merger and Internalization• But why is the merged firm’s pollution level
of xm = 2 efficient?
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Merger and Internalization• But why is the merged firm’s pollution level
of xm = 2 efficient?• The external cost inflicted on the fishery is
xf, so the marginal external pollution cost isMC fx
E .
![Page 87: Ch 32 Externalities](https://reader035.vdocument.in/reader035/viewer/2022062819/577cc00e1a28aba7118eb017/html5/thumbnails/87.jpg)
Merger and Internalization• But why is the merged firm’s pollution level
of xm = 2 efficient?• The external cost inflicted on the fishery is
xf, so the marginal external pollution cost is• The steel firm’s cost of reducing pollution is MC fx
E .
MC x xm ( ) ( ).2 4
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Merger and Internalization• But why is the merged firm’s pollution level
of xm = 2 efficient?• The external cost inflicted on the fishery is
xf, so the marginal external pollution cost is
• The steel firm’s cost of reducing pollution is
• Efficiency requires
MC fxE .
MC x xm ( ) ( ).2 4
MC MC x f xxE m ( ) ( ).2 4
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Merger and Internalization
• Merger therefore internalizes an externality and induces economic efficiency.
• How else might internalization be caused so that efficiency can be achieved?
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Coase and Production Externalities
• Coase argues that the externality exists because neither the steel firm nor the fishery owns the water being polluted.
• Suppose the property right to the water is created and assigned to one of the firms. Does this induce efficiency?
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Coase and Production Externalities• Suppose the fishery owns the water.• Then it can sell pollution rights, in a
competitive market, at $px each.• The fishery’s profit function becomes
F f xf x p f f xf p x( , ) . 2
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Coase and Production Externalities• Suppose the fishery owns the water.• Then it can sell pollution rights, in a competitive
market, at $px each.• The fishery’s profit function becomes
• Given pf and px, how many fish and how many rights does the fishery wish to produce? (Notice that x is now a choice variable for the fishery.)
F f xf x p f f xf p x( , ) . 2
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Coase and Production Externalities
Ff
Fx
fp f x
xf p
2 0
0
F f xf x p f f xf p x( , ) . 2
The profit-maximum conditions are
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Coase and Production Externalities
Ff
Fx
fp f x
xf p
2 0
0
F f xf x p f f xf p x( , ) . 2
The profit-maximum conditions are
and these give f px p p
xS f x
** . 2
(fish supply)(pollutionright supply)
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Coase and Production Externalities• The steel firm must buy one right for every
unit of pollution it emits so its profit function becomes
• Given pf and px, how much steel does the steel firm want to produce and how many rights does it wish to buy?
S s xs x p s s x p x( , ) ( ) . 2 24
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Coase and Production Externalities
Ss
Sx
sp s
xx p
2 0
2 4 0( )
S s xs x p s s x p x( , ) ( ) . 2 24The profit-maximum conditions are
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Coase and Production Externalities
Ss
Sx
sp s
xx p
2 0
2 4 0( )
S s xs x p s s x p x( , ) ( ) . 2 24The profit-maximum conditions are
and these give s p
x p
s
Dx
*
* .
24
2
(steel supply)
(pollutionright demand)
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Coase and Production ExternalitiesIn a competitive market for pollution rightsthe price px must adjust to clear the marketso, at equilibrium,
x p p p xDx
f x S* *. 42
2
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Coase and Production ExternalitiesIn a competitive market for pollution rightsthe price px must adjust to clear the marketso, at equilibrium,
x p p p xDx
f x S* *. 42
2
The market-clearing price for pollutionrights is thus p p
xf2 83
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Coase and Production ExternalitiesIn a competitive market for pollution rightsthe price px must adjust to clear the marketso, at equilibrium,
x p p p xDx
f x S* *. 42
2
The market-clearing price for pollutionrights is thus p p
xf2 83
and the equilibrium quantity of rightstraded is x x p
D Sf* * .
163
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Coase and Production Externalitiess p f p x x ps
x D Sf* ; * ; * * ;
2
163
p px
f2 83
.
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Coase and Production Externalitiess p f p x x ps
x D Sf* ; * ; * * ;
2
163
p px
f2 83
.
So if ps = 12 and pf = 10 thens f x x pD S x* ; * ; * * ; . 6 4 2 4
This is the efficient outcome.
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Coase and Production Externalities• Q: Would it matter if the property right to the
water had instead been assigned to the steel firm?
• A: No. Profit is linear, and therefore quasi-linear, in money so Coase’s Theorem states that the same efficient allocation is achieved whichever of the firms was assigned the property right. (And the asset owner gets richer.)
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The Tragedy of the Commons• Consider a grazing area owned “in common”
by all members of a village.• Villagers graze cows on the common.• When c cows are grazed, total milk
production is f(c), where f’>0 and f”<0.• How should the villagers graze their cows so
as to maximize their overall income?
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The Tragedy of the Commons
c
Milkf(c)
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The Tragedy of the Commons
• Make the price of milk $1 and let the relative cost of grazing a cow be $pc. Then the profit function for the entire village is
• and the village’s problem is to
( ) ( )c f c p cc
max ( ) ( ) .c
cc f c p c
0
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The Tragedy of the Commonsmax ( ) ( ) .c
cc f c p c
0
The income-maximizing number of cowsto graze, c*, satisfies
f c pc( )
i.e. the marginal income gain from thelast cow grazed must equal the marginalcost of grazing it.
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The Tragedy of the Commons
c
Milkf(c)pcc
slope =f’(c*)
c*
slope= pc
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The Tragedy of the Commons
c
Milkf(c)pcc
slope =f’(c*)
c*
slope= pc
Maximal incomef(c*)
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The Tragedy of the Commons
• For c = c*, the average gain per cow grazed is
• because f’ > 0 and f” < 0.
( *)*
( *) **
( *)*
cc
f c p cc
f cc
pcc
0
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The Tragedy of the Commons
c
Milkf(c)pcc
slope =f’(c*)
c*
f cc
pc( *)*
f(c*)
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The Tragedy of the Commons• For c = c*, the average gain per cow grazed is
• because f’ > 0 and f” < 0. So the economic profit from introducing one more cow is positive.
• Since nobody owns the common, entry is not restricted.
( *)*
( *) **
( *)*
cc
f c p cc
f cc
pcc
0
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The Tragedy of the Commons
• Entry continues until the economic profit of grazing another cow is zero; that is, until
( ) ( ) ( ) .cc
f c p cc
f cc
pcc
0
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The Tragedy of the Commons
c
Milkf(c)pcc
slope =f’(c*)
c*
f cc
pc( )
f(c*)
c
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The Tragedy of the Commons
c
Milkf(c)pcc
slope =f’(c*)
c*
f cc
pc( )
f(c*)
The commons are over-grazed, tragically.c
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The Tragedy of the Commons
• The reason for the tragedy is that when a villager adds one more cow his income rises (by f(c)/c - pc) but every other villager’s income falls.
• The villager who adds the extra cow takes no account of the cost inflicted upon the rest of the village.
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The Tragedy of the Commons
• Modern-day “tragedies of the commons” include– over-fishing the high seas– over-logging forests on public lands– over-intensive use of public parks; e.g.
Yellowstone.– urban traffic congestion.