1. Chapter 34
Externalities

2. Externalities
An externality is a cost or a benefit imposed upon someone by actions taken by others.
A benefit caused by someone else (externally imposed ) is a positive externality.
An externally imposed cost is a negative externality.

3. Examples of Negative Externalities
Air or water pollution.
Loud parties next door (to which you’re not invited).
Traffic jams.
Passive smoking.
Increased insurance premiums because others drink, smoke or drive carelessly.
A perfume worn by the person next to you to which you have an allergic reaction.

4. Examples of Positive Externalities
A pleasant perfume worn by the person seated next to you.
Flowers in your neighbour’s garden which look pretty from your window.
Improved driving habits that reduce accident risks.
A shift of travelling from cars to public transport which reduces air pollution.

5. Externalities and Efficiency
The whole argument why competitive markets result in Pareto efficiency presupposes that there are no externalities.
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.

6. Inefficiency & Negative Externalities
Consider two agents, A and B, and two commodities, money and smoke.
A is a smoker - both smoke and money are good( thing)s for A.
B doesn’t smoke and doesn’t like smoke. Money is a good and smoke is a bad for B.
They share a room and therefore breathe the same (equally smoke-filled) air.

7. Agent A is endowed with yA SEK.
Agent B is endowed with yB SEK.
Smoke intensity is measured on a scale from 0 (no smoke) to 1 (maximum concentration).

8. Smoke
Money and smoke are both goods for Agent A. 1 OA yA
moneyA

9. Smoke 1
Better OA yA mA

10. Smoke
But smoke is a “bad” for B,
not a “good”. 1
Better OB yB
MoneyB

11. 1 mB yB OB Turn the diagram for B around to make an Edgeworth Box
Smoke 1
Better mB yB OB

12. What are the efficient allocations of smoke and money?1 1
Smoke OA mB mA OB

13. Efficient allocations of smoke and money.1 1
Smoke OA yA yB OB mA mB

14. Efficient allocations
Smoke
Smoke 1 1 OA yA yB OB mA mB

15. Suppose there is no means by which money can be exchanged for changes in smoke level.
What then is A’s most preferred allocation?
Is this allocation efficient?

16. 1 1 OA yA yB OB mA mB Smoke Smoke The choices
A has – income yA and some amount of smoke 1 1 OA yA yB OB mA mB

17. A’s most preferred choice is income yA and as much smoke as possible
A’s most preferred choice is income yA and as much smoke as possible. This choice is inefficient 1 1
Smoke
Smoke OA yA yB OB mA mB

18. B’s most preferred choice is income yB and no smoke
B’s most preferred choice is income yB and no smoke. This choice is inefficient too.
Smoke
Smoke 1 1 OA yA yB OB mA mB

19. If property rights are introduced:
So if A and B cannot trade money for changes in smoke intensity, then the outcome is inefficient.
There is no market for smoke-filled or smoke-free air because there are no property rights.
If property rights are introduced:
Either A can have the right to smoke which is tantamount to giving A ownership of the air in the room.
Or B can have the right to breathe smoke-free air which is tantamount to giving the ownership to B.

20. 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?
Let p*s be the price paid by Agent A to Agent B in order to be allowed to create a smoke intensity of s.

21. A line from (yA,0) with the slope -p is a budget constraint for A.
Smoke
Smoke 1 1
Initial endowments OA yA yB OB mA mB

22. 1 1 OA yA yB OB mA mB Smoke Smoke Both agents gain and there is a
p*sA transferred from A to B
Smoke
Smoke 1 1
Both agents
gain and
there is a
positive
amount of
smoking. sA OA yA yB OB mA mB

23. 1 1 OA yA yB OB mA mB Smoke Smoke Both agents gain and there is a
positive
amount of
smoking. sA OA yA yB OB mA mB

24. Internalising externalities
At the smoke level s, A compensates B for the smoke – bears the cost of the external negative effect caused by A’s smoking.
Making a producer of an externality to bear the full external cost or to enjoy the full external benefit is called internalizing the externality.

25. Suppose instead that A is assigned the ownership of the air in the room.
B can now pay A to reduce the smoke intensity.
How much smoking will there be?
How much money will B pay A?

26. Smoke
Smoke 1 1 OA yA yB OB mA mB

27. Smoke
Smoke 1 1 OA yA yB OB mA mB

28. Smoke
Smoke
p*sB 1 1 sB OA yA yB OB mA mB

29. 1 1 OA yA yB OB mA mB Smoke Smoke p(sB) Both agents gain and
there is a
reduced
amount of
smoking. sB OA yA yB OB mA mB

30. 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.
A general problem in cases like this is that both parties may consider that they should have the property rights.

31. 1 1 sA ¹ sB and the net incomes also depend on who “owns the air” OA
Smoke
Smoke
p(sB)
p(sA) 1 1 sB
sA ¹ sB
and the net
incomes also
depend on who
“owns the air” sA OA yA yB OB mA mB

32. 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?
If for both agents, preferences are quasilinear in money; U(m,s) = m + f(s), we have seen (exc. 6.3) that demand for smoke doesn’t depend on income.
In this special case, the amount of smoke at the efficient point does not depend on who has the property right.

33. 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.

34. Production Externalities
A chemical factory produces jointly herbicides and pollution.
The pollution causes allergies and asthma in children living nearby.
The local health clinic treats the children.
ph is the market price of herbicides.
cx is the medical cost that come from an increase of pollution by one unit.
For simplicity we ignore the “intangible costs” of illness – the argument would be analogous if we can attach a value to the loss of well-being.

35. ch(h,x) is the chemical firm’s cost of producing s units of herbicide jointly with x units of pollution.
If the chemical 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 maximise this function.

36. First-order maximization conditions
In other words, production is carried on up to the point where the marginal cost of increasing production of herbicides is equal to the price and where the marginal gain from increasing pollution is zero.

37. is the rate at which the firm’s
internal production cost goes down as the
pollution level rises
Conversely
is the marginal cost to the firm of pollution reduction.
The marginal benefit to the firm of pollution production is zero since it does not pay the health care costs.

38. But the marginal social cost is cx
If the firm had to pay the health care costs it caused it it would only increase
production of pollution until
If we assume that the marginal benefit of increasing pollution is decreasing, this means that a firm that was made responsible for the damage it caused would produce less pollution (and less herbicides).
Because the cost of treating allergies is external to the firm, it overproduces.
An emissions tax of cx would increase efficiency and welfare.

39. Production Externalities: A numerical example:
A foundry produces steel (s) and pollution (x)
Its cost function is:
cS(s,x) = s2 + (x - 4)2
Assume that pS = 12
The profit function will be:
Π(s, x) = 12s - s2 - (x - 4)2
and the first order conditions for maximum are:
Π’s(s, x) =12 -2s = 0 s = 6
Π’x(s, x) =2(x-4) = 0 x = 4
Π(6, 4) = 72 – 36 – 0 = 36

40. Downstreams from the foundry is a fishery whose production depends (negatively) on the level of pollution in the water.
The cost to the fishery of catching f units of fish (which it can sell at a price of pF = 10) when the steel mill emits x units of pollution is cF(f, x) = f2 + xf
Given f, cF(f,x) increases with x; i.e. the steel firm inflicts a negative externality on the fishery.

41. The fishery’s profit function is
and the first order condition
Π’F = f - x = 0
Without any pollution f = 5 and Π = 25
With a pollution of x=4, f = 3 and Π = 9
Thus, production and profits are lower in the presence of pollution. This is the external cost of the pollution.

42. 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 = 45.
Is 45 the largest possible total profit that can be achieved?
What happens if the two firms merge?

43. Merger and Internalization
Profits of the new firm are.
First order conditions for maximum:
12-2s = 0 (1)
10 – 2f – x = 0 (2)
-2(x-4)- f = 0 (3)
(1)  s = 6
(2)  x = 10 –2 f (4)
(3) & (4)  -2(10-2f-4) = f  f = 4; x = 2
Note that: and

44. And the merged firm’s maximum profit level is
Without merger, total profits were 45 and pollution was 4.
After a merger, profits are 48 and pollution is 2.
The merger has internalised the externality.
Efficiency has increased.
Pollution is decreased.

45. In the merged firm the profit function is
The marginal cost of pollution is
The merged firm’s marginal pollution cost
is larger because it faces the full cost of
its own pollution through increased costs
of production in the fishery, so less
pollution is produced by the merged firm.

46. Merger and Internalization
How else might internalization be caused so that efficiency can be achieved?
Property rights (create a market)
Taxes
Tradeable emission quotas
Restrictions on production or emissions

47. Coase argues that the externality exists because neither the steel firm nor the fishery owns the water being polluted.
Property right to the water can be created and assigned to one of the firms. This would induce efficiency (and benefit whoever got the property rights).
To give the fishery the rights would agree with the Polluter Pays Principle

48. Tradeable emissions quotas:
The government sets a target for reduction of emissions.
Each firm is given or allowed to buy a certain quantity of emission-rights.
A firm that emits less than its quota can sell the right to emit to somebody else.
Reductions will be made where it is cheapest to make them.

49. Taxing pollution
Assume that the foundry has to pay a tax of t*x where t is a tax rate.
If t is set so that at the socially optimal level of x, the MC of polluting to the foundry will be equal to the social MC and it will reduce pollution to the optimal level.
In the example, set t = 4 and solve the foundry’s profit maximisation problem!
This kind of tax is called a Pigouvian tax.
They are good if they are set correctly but to set them correctly requires knowledge of the optimal level of pollution.

50. 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?

51. The Tragedy of the Commons
Milk
f(c)
Slope = f(c)/c= AP
cows
The marginal and average products decrease when the number of cows increase.

52. The profit function for the entire village is
Assume that:
the price of milk is 10
the cost of grazing a cow is pc.
The profit function for the entire village is
and the village’s problem is to

53. To maximise the village’s income the number of cows, c
To maximise the village’s income the number of cows, c*, should be such that f’(c) = pc
The marginal product from the last cow grazed
must equal the marginal cost of grazing it.
But for each villager it pays to buy another cow until
the average product is equal to pc
If AP is decreasing, MP>AP. So when AP(c) = pc,
MP(c) < pc.
The common pasture will be overgrazed if:
each villager considers only their own cost and income.
there is no restriction on entry

54. Will this happen? Modern-day “tragedies of the commons” include
over-fishing the oceans
Air pollution, greenhouse gases and congestion from cars.
BUT there are other commons where tragedies have been avoided.
The conventional economist’s advice is “privatise and introduce markets”.
BUT different societies have handled the preservation of common resources also through institutional setups other than private property and markets.

55. Elinor Ostrom, Nobel laureate 2009
“Elinor Ostrom has challenged the conventional wisdom that common property is poorly managed and should be either regulated by central authorities or privatized. Based on numerous studies of user-managed fish stocks, pastures, woods, lakes, and groundwater basins, Ostrom concludes that the outcomes are, more often than not, better than predicted by standard theories. She observes that resource users frequently develop sophisticated mechanisms for decision-making and rule enforcement to handle conflicts of interest, and she characterizes the rules that promote success-ful outcomes.”
(Quoted from the statement to the Public by the Royal Academy of Sciences)

56. At
you will find two documents. The part about Ostrom in “Information for the public”
is included in the course literature. Read it!
If you are a bit more interested, also read the other document “Scientific background”.

57. She has studied user-managed
Ostrom builds on
own and other case studies of governance of Common Pooled Resources
Game-theory and experiments.
She has studied user-managed
Fish stocks
Pastures
Woods
Lakes
Groundwater basins

58. A CPR is a resource to which more than one individual has access but where each person’s consumption reduces availability of the resource to others.
It is not possible to lay down one rule for managing all CPRs. It depends the technological nature of the resource and the institutional context that has evolved over time.
Privatisation works in some cases but may not work where it is difficult for users to agree on the terms. (Underground water basins or oil pools).
Government intervention may work in some cases, particularly with large scale CPRs but may also ”create more chaos than order” if central government lacks local information or legitimacy.

59. A third option: Retain the resource as common property and let the users create their own system of governance.
A lot of cases show local communities succesfully managing CPRs but their are also failures.
The kinds behaviour observed in governance of CPRs has also been found in experiments.
A key element is sanctions: economic theory has to ask why individuals are willing to undertake costly monitoring and sanctioning. Can’t be explained only by self-interest.
Another central issue is reciprocity.

60. When does local governance work well?
(i) rules should clearly define who has what entitlement,
(ii) adequate conflict resolution mechanisms should be in place
(iii) an individual’s duty to maintain the resource should stand in reasonable proportion to the benefits.
(iv) monitoring and sanctioning should be carried out either by the users themselves or by someone who is accountable to the users.
(v) sanctions should be graduated, mild for a first violation and stricter as violations are repeated.
(vi) governance is more successful when decision processes are democratic, in the sense that a majority of users are allowed to participate in the modification of the rules and when
(vii) the right of users to self-organize is clearly recognized by outside authorities.
vii) In the case of larger common-pool resources: organization in the form of multiple layers of nested enterprises, with small local CPRs at the base level.