1

Externalities
 Sometimes costs or benefits that result from an activity accrue to people not directly involved in the activity.
 These are called external costs or external benefits
-externalities for short.
2

Example 12.1.
 Sara is an accomplished classical violinist.
 Her neighbor Tom is a fan of classical violin music, and on summer evenings enjoys listening to Sara play in her garden.
 For Tom, Sara's music is a positive externality.
 If Sara plays only in response to her own costs and benefits, will the amount of time she plays be socially optimal?
3

Example 12.1.
 If Sara plays in response to her own costs and benefits, she will continue to play until the marginal benefit of playing another minute is equal to the marginal cost.
 But since Tom also benefits from her playing, at that point the total marginal benefit of playing another minute will be greater than the marginal cost.
4

Example 12.1.
 Thus, if Sara plays in response to her own costs and benefits, Sara plays too little.
($/minute)
Marginal Cost to Sarah
0.65
0.50
Marginal Benefit to Sarah
T*
Minutes
MB to Tom
5

Example 12.2.
 Sara is an accomplished classical violinist.
 Her neighbor Harry hates the sound of violin music, and on summer evenings becomes distressed when Sara plays in her garden.
 For Harry, Sara's music is a negative externality.
 If Sara plays only in response to her own costs and benefits, will the amount of time she plays be socially optimal?
6

Example 12.1.
 If Sara plays in response to her own costs and benefits, she will continue to play until the marginal benefit of playing another minute is equal to the marginal cost.
 But since Harry also incurs costs from her playing, at that point the marginal benefit of playing another minute will be greater than their combined marginal costs.
7

Example 12.2.
 Thus, if Sara plays in response to her own costs and benefits, Sara plays too much.
($/minute) Marginal Cost to Sarah
0.75
0.50
T*
Marginal Benefit to Sarah
Minutes
MC to Harry
8

Externalities and activity
 Negative externalities => too much activity
 Positive externalities => too little activity
9

Example 12.3.
 Smith can produce with or without a filter on his smokestack.
 Production without a filter results in greater smoke damage to Jones.
10

Example 12.3.
Gains to Smith
Damage to Jones
Smith produces with filter
$200/week
$35/week
Smith produces without filter
$245/week
$85/week
If Smith is not liable for smoke damages and if the two parties can negotiate costlessly with one another, will he install a filter?
11

Example 12.3.
Gains to Smith
Damage to Jones
Smith produces with filter
$200/week
$35/week
Smith produces without filter
$245/week
$85/week
Total economic surplus goes up if Smith installs the filter:
$200-$35=$165 > $245-$85=$160.
The filter costs $245-$200=$45.
Smith doesn't have to install it, but if Jones pays him at least $45, he will gladly do so.
And since the filter results in savings of
$84-$35=$50 for Jones, he will pay Smith to install the filter.
12

The Coase Theorem
If property rights are fully assigned and if people can negotiate costlessly with one another, they will always arrive at efficient solutions to problems caused by externalities.
Ronald Coase: 1991 Nobel
Laureate in Economics
Additional readings:
Posner, Richard A. (1993): “Nobel Laureate Ronald Coase and Methodology,”
Journal of Economic Perspectives , 7(4): 195-210.
“Of Bees and Lighthouses: Schools Brief,” The Economist , Feb 23, 1991, p.72.
13

Example 12.3.
 Traditional (pre-Coase) view:
 Smith is the perpetrator (the person who committed a crime), Jones is the victim.
 If it is Smith's smoke that is causing the damage to
Jones, why should Jones pay Smith to install a filter on his smokestack?
14

Example 12.3.
 Coase’s insight was that externalities are purely reciprocal.
 The smoke harms Jones, true enough.
 But to restrain Smith from producing smoke would harm Smith.
 The two parties have a shared interest in achieving the outcome that is least costly overall.
15

Benefit to all when the pie is larger
Smith
Jones
16

Example 12.4.
Ted and Bill can live together in a two-bedroom apartment for $500/mo…
17

Example 12.4.
…or each rent a one-bedroom apartment for $300/mo.
18

Example 12.4.
If the rent were the same, they would be indifferent between living together or separately, except for one problem:
Ted likes to practice his trumpet late at night and this will disturb Bill's sleep.
19

Example 12.4.
 Ted would pay up to $150/mo rather than reschedule his playing.
 Bill would pay up to $80 per month not to have his sleep disturbed.
Will they live together or separately?
20

Example 12.4.
 The question is whether the benefits of joint living exceeds the costs.
 The benefit is the $100 per month reduction in rent.
What is the least costly accommodation to the trumpet problem?
21

Example 12.4.
 If they live together
 Cost to Ted of stopping playing: $150/mo
 Cost to Bill of tolerating the noise: $80/mo
 So the least costly solution is for Bill to put up with the noise (since $80 < $150).
 Since this cost ($80) is less than the $100/mo gain, they should live together.
22

Example 12.5.
 In the preceding example, what is the largest rent Bill would be willing to pay if the two were to live together?
If Bill were to live alone, he would pay $300/mo and suffer no trumpet noise.
Since the noise costs him $80/mo, the most he would be willing to pay for the shared apartment is
$300 - $80 = $220.
23

Example 12.6.
 How should Ted and Bill split the $500/mo rent if they agree that each should benefit equally from living together?
Their total gain from living together is
$100 - $80 = $20/mo.
If Ted pays $290/mo and Bill pays $210/mo, each will be
$10/mo better off than if he were to live alone.
24

Costly negotiations
 It is often impractical to negotiate solutions to the problems created by externalities.
 Hospital patients, for example, are unable to negotiate with passing motorists about not blowing their horns.
 In such cases, the law tries to impose the burden of adjustment on the party that can accomplish it at lowest cost.
25

Costly negotiations
Not blowing his horn is a cost to the motorist, but a benefit to the patient.
Because peace and quiet is especially valuable for hospital patients, the law prohibits horn blowing in the vicinity of hospitals.
26

Costly negotiations
In non-hospital zones, the law is more liberal in its tolerance of noise.
In many cities, there are 11 PM noise curfews on weekdays, midnight curfews on weekends.
For those who are interested in law and economics:
Bouckaert, Boudewijn and De Geest, Gerrit (eds.), Encyclopedia of
Law and Economics, Cheltenham, Edward Elgar, 2000
27

Example 12.7.
The Right to an Unobstructed View
 Lehman owns a house overlooking the lake, from which he enjoys a commanding sunset view.
28

Example 12.7.
The Right to an Unobstructed View
 Now Martin purchases the property below Lehman's and is considering which of two houses to build:
 a one-story house that would leave Lehman's view intact;
 or a two-story design that would completely block
Lehman's view.
Lehman
Martin
29

Example 12.7.
The Right to an Unobstructed View
 Suppose the gain to Lehman from an unobstructed view is 100, the gain to Martin from having a one-story house is 200, and the gain to Martin from a two-story house is 280.
 If the laws of property let people build houses of any height they chose, and if negotiation between property owners were costless, which of the two houses would
Martin build?
Lehman
Martin
30

Example 12.7.
The Right to an Unobstructed View
 Value of view to Lehman: 100
 Value of second story to Martin: 280-200=80
 The increase in Martin's gain from having the taller house is 80, which is 20 less than the cost to Lehman from the loss of his view.
 The efficient outcome is thus for Martin to build the one-story house.
 And that is exactly what would happen if the two parties could negotiate costlessly.
31

Example 12.7.
The Right to an Unobstructed View
 Rather than see Martin build the taller house, it will be in Lehman's interest to compensate Martin for choosing the shorter version.
 To do so, he will have to give Martin at least 80.
 The most Lehman would be willing to pay is 100, since that is all the view is worth to him.
 For some payment P, where 80  P  100, Lehman will get to keep his view.
32

Example 12.7.
The Right to an Unobstructed View
 Suppose, however, that negotiations between the two parties were impractical.
 Martin would then go ahead with the two-story house, since that is the version he values most.
 By comparison with the one-story design, Martin would gain 80, but Lehman would lose 100.
 The optimal structure of property rights in this particular example would be to prohibit any building that blocks a neighbor's view.
33

Example 12.7.
The Right to an Unobstructed View
 If the valuations assigned by the parties were different, a different conclusion might follow.
 If, for example, Martin valued the two-story house at
300 and Lehman valued the view at only 80, the optimal structure of property rights would be to allow people to build to whatever height they chose.
34

Modified Coase Theorem
 The optimal structure of property rights is the one that places the burden of adjustment (either the loss of a view or the loss of a preferred building design) on the party that can accomplish it at the lowest cost.
 As a practical matter, the laws of property in many jurisdictions often embody precisely this principle.
35

Modified Coase Theorem

36

Modified Coase Theorem
 Zoning laws in cities where there is less to look at are generally much more liberal in the kinds of buildings they permit.
37

Modified Coase Theorem
 But even in cities that have no special view to protect at all, zoning laws generally limit the fraction of the lot that can be occupied by manmade structures.
38

Example 12.8. Taxing Negative Externalities
 Two firms, X and Y, have access to five different production processes, each one of which has a different cost and gives off a different amount of pollution.
Process
(daily smoke)
Cost to Firm X
Cost to Firm Y
A
(4 tons)
200
50
B
(3 tons)
290
80
C
(2 tons)
700
140
D
(12 tons)
1300
230
E
(0 ton)
2100
325
If pollution is unregulated, and negotiation between the firms and their victims is impossible, each firm will use A, the least costly of the five processes.
Each will emit 4 tons of pollution per day, for a total pollution of 8 tons/day.
39

Example 12.8. Taxing Negative Externalities
 The city council wants to cut smoke emissions by half.
To accomplish this, they are considering two options.
A. Require each firm to curtail its emissions by half.
B. Set a tax of T on each ton of smoke emitted each day.
How large would T have to be in order to curtail emissions by half?
And how would the total costs to society compare under the two alternatives?
40

Example 12.8. Taxing Negative Externalities
A: If each firm is required to cut pollution by half, each must switch from process A to process C.
The result will be two tons/day of pollution for each firm.
Process
(daily smoke)
Cost to Firm X
Cost to Firm Y
A
(4 tons)
200
50
B
(3 tons)
290
80
C
(2 tons)
700
140
D
(1 tons)
1300
230
E
(0 ton)
2100
325
The cost of the switch for firm X will be
700/day-200/day=500/day.
The cost to Y will be 140/day-50/day=90/day,
So total cost for the two firms = 590/day.
41

Example 12.8. Taxing Negative Externalities
B: How will each firm respond to a tax of T per ton of pollution?
Switching to the next process will cut pollution by 1 ton per day and save tax of T/day.
If cost of switching to the next process is less than or equal to T, it will switch, otherwise not.
42

Example 12.8. Taxing Negative Externalities
 T= 50/ton: Firm X would stick with process A. Firm Y will switch to process B.
Process
(daily smoke)
Cost to Firm X
Cost to Firm Y
A
(4 tons)
200
50
B
(3 tons)
290
80
C
(2 tons)
700
140
D
(1 tons)
1300
230
E
(0 ton)
2100
325
A tax of 50/ton thus does not produce the desired 50 percent reduction in pollution.
43

Example 12.8. Taxing Negative Externalities
 T= 91/ton. X will adopt process B, Y will adopt process
D.
Process
(daily smoke)
Cost to Firm X
Cost to Firm Y
A
(4 tons)
200
50
B
(3 tons)
290
80
C
(2 tons)
700
140
D
(1 tons)
1300
230
Total emissions will be the desired 4 tons/day.
E
(0 ton)
2100
325
Cost to firm X will be 290/day-200/day = 90/day.
Cost to firm Y will be 230/day-50/day = 180/day.
Total cost for both firms is thus only 270/day, or 320/day less than the cost of having each firm cut pollution by half.
44

Example 12.8. Taxing Negative Externalities
 Note that the taxes paid by the firm are not included in our reckoning of the social costs of the tax alternative, because this money is not lost to society.
 It can be used to reduce whatever taxes would otherwise have to be levied on citizens.
45

Example 12.9. Pollution Permits
 Similar to the preceding example but now the government issues pollution permits to the two firms, allowing them to generate 4 tons of smoke daily, in total.
 Will the pollution generated by the two firms change with the different allocation of permits?
46

Example 12.9. Pollution Permits
 Similar to the preceding but now the government issues pollution permits to the two firms, allowing them to generate 4 tons of smoke daily, in total.
 Suppose each firm is given permits to generate 2 tons of smoke.
Process
(daily smoke)
Cost to Firm X
Cost to Firm Y
A
(4 tons)
200
50
B
(3 tons)
290
80
C
(2 tons)
700
140
D
(1 tons)
1300
230
E
(0 ton)
2100
325
By moving from C to B, Firm X will generate 1 more ton of smoke but will save a cost of $410. By moving from C to D, Firm Y will incur a cost of $90. Negotiation will ensure the new allocation (3 tons for firm
X, and 1 ton for firm Y)
47

The Tragedy of the Commons
48

Example 12.10
 A village has five residents, each of whom has accumulated savings of $100.
 Each villager has two investment opportunities:
1.
Buy government bond for $100 that pays 12% interest per year.
2.
Buy a year-old steer for $100, send it onto the commons to graze, then sell it after one year.
49

Example 12.10
 The Relationship Between Herd Size, Selling Price, and
Profit per Steer
Profit per steer ($) Number of steers on the commons
3
4
1
2
5
Price per 2-year- old steer ($)
120
116
114
112
110
20
16
14
12
10
If each person decides individually how to invest, how many steers will be sent onto the commons?
50

Example 12.10
If each person decides individually how to invest, how many steers will be sent onto the commons?
Number of steers on the commons
1
2
3
4
5
Price per 2-year- old steer ($)
120
116
114
112
110
Profit per steer ($)
20
16
14
12
10
 Opportunity cost of investing in steer = 12
 Send steer if and only if price of 2-year-old steer is at least 112
 Four of the villagers send 1 steer, and hence a total of 4 steers.
 Total village income = 12 + 4(12) = 60
51

Example 12.10
In the preceding example, what is the socially optimal number of steers?
Number of steers on the commons
1
2
3
4
5
Price per 2-year- old steer ($)
120
116
114
112
110
Value of herd ($)
120
232
342
448
550
 Decision rule for socially optimal investment:
Send another steer only if the value of the herd increases by at least 12.
 Thus, we should send a second steer but not a third. Total income
= $32 + $36 = $68
52

Tragedy of commons
 The problem with private decisions is that no individual has any incentive to take into account that an extra steer will eat grass that otherwise would have been available to the steers already on the commons.
 The tragedy of the commons is thus a type of externality.
53

Example 12.11.

If each has a straw and each knows that the other is self-interested, will the rate at which they consume the milkshake be optimal?
54

Example 12.11.
 Each knows that any part of the milkshake he doesn't drink will be drunk by the other.
 So each consumes at a faster rate than he would if he had half the shake all to himself.
55

Examples of Tragedies of the Commons
Harvesting timber on public land.
Each tree cutter knows that a tree not harvested this year will be bigger, and hence more valuable, next year.
But he also knows that if he doesn't cut the tree down this year, someone else will.
56

Examples of Tragedies of the Commons
Picking blackberries in a public park
Each individual knows that the blackberries would taste better if allowed to ripen for another week.
But each also knows that blackberries not eaten today may not be there next week.
57

Examples of Tragedies of the Commons
Harvesting whales in international waters
Each individual whaler knows that harvesting an extra whale reduces the breeding population of whales and hence the size of future whale populations.
But he also knows that any whale he fails to harvest today will just be taken by some other whaler.
58

Examples of Tragedies of the Commons
Pollution
Each individual polluter has no incentive to take into account the cost his pollution imposes on others.
59

Tragedies of the Commons
 Clearly defined property rights are one way to solve the tragedy of the commons
60

Example 12.12. (Chapter 1-4)
 Once a week, Smith purchases a six-pack of cola and puts it in his refrigerator for his two children. He invariably discovers that all six cans are gone on the first day. Jones also purchases a six-pack of cola once a week for his two children, but unlike Smith, he tells them that each may drink no more than three cans. If the children use cost-benefit analysis each time they decide whether to drink a can of cola, explain why the cola lasts much longer at Jone’s house than at Smith’s .
61

Example 12.12. (Chapter 1-4)
 At Smith’s house, each child knows that the cost of not drinking a can of cola now is that it is likely to end up being drunk by his sibling. Each thus has an incentive to consume rapidly to prevent the other from encroaching on his share.
 Jones, by contrast, has eliminated that incentive by making sure that neither child can drink more than half the cans. This step permits his children to consume at a slower, more enjoyable pace.
62

Defined property rights as a solution to tragedy of the commons
Weyerhauser doesn't cut trees down too quickly on its own land.
Weyerhaeuser is an international forest products company with annual sales of
$22.6 billion. It was founded in 1900 and currently employs about 54,000 people in 18 countries.
63

Defined property rights as a solution to tragedy of the commons
People don't harvest blackberries too soon from their backyard garden.
64

Defined property rights as a solution to tragedy of the commons
People don't dump toxic wastes into their own swimming pools.
65

Regulation as a solution to tragedy of the commons
66

Regulation as a solution to tragedy of the commons
67

Regulation as a solution to tragedy of the commons
68

Regulation as a solution to tragedy of the commons
69

Example 12.13
 In the cattle-grazing economy considered earlier, suppose there is now a 25% tax on income earned from cattle.
 If people decide individually between bonds and cattle, how many steers will be sent onto the commons?
70

Example 12.13
With a 25% tax on income from cattle, only 2 steers will be sent onto the commons, and this is the socially optimal number.
Number of steers on the commons
3
4
5
1
2
Price per 2-year- old steer ($)
120
116
114
112
110
After-Tax Profit per steer ($), with 25% tax on cattle income
15
12
10.50
9
7.50
Total income = 3(12) + 2(12) + 8 = 68
(bonds) (cattle) (tax)
71

Tragedy of the commons
 One of the continuing sources of inefficiency in modern economies involves the allocation of resources that
.
 Several species of whales have been hunted to near extinction because international laws of property are insufficient to restrain individual incentives to kill whales.
 The Mediterranean Sea has long had serious problems with pollution, because none of the many nations that border it has an economic incentive to consider the effects of its discharges on other countries.
72

Example: Why do football players take anabolic steroids?
 Smith and Jones are competing for a single position and a $1 million contract.
73

Example: Why do football players take anabolic steroids?
Smith
Don’t take steroids
Take steroids
Don’t take steroids
Jones
Second best for each
Take steroids
Best for Jones
Worst for Smith
Best for Smith
Worst for Jones
Third best for each
•Dominant strategy for each yields the third best outcome
•This prisoner’s dilemma outcome is the attraction of rules banning performance enhancing drugs.
74

Positional Arms Races and Positional Arms
Control Agreements
 Positional Externality
 When an increase in one person’s performance reduces the expected reward of another in situations in which reward depends on relative performance
 Positional Arms Race
 A series of mutually offsetting investments in performance enhancement that is stimulated by a positional externality
75

Positional Arms Races and Positional Arms
Control Agreements
 Positional Arms Control Agreements
 An agreement in which contestants attempt to limit mutually offsetting investments in performance enhancements
 Campaign spending limits
 Roster limits
 Arbitration agreements
 Mandatory starting dates for kindergarten
76

Positional Arms Races and Positional Arms
Control Agreements
 Social Norms as Positional Arms Control Agreements
 Nerd norms
 Good grades vs. all study too hard
 Fashion norms
 Avant-garde status vs. excessive body mutilation
 Norms of taste
 Catching attention vs. too much nudity
 Norms against vanity
 Cosmetic/reconstructive surgery vs. Michael
Jackson
77

End
78