Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Externalities
Public Economics
Carlo Fiorio
Bocconi University
[email protected]
http://www.econpubblica.uni-bocconi.it/fiorio
Academic Year 2006/2006
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Today’s questions
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What is an externality?
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Why are externalities making the market inefficient?
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What are the solutions available when externalities arise?
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
What is an externality?
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An externality is an action by one agent which affects
directly the well-being or production possibilities of other
agents, but is chosen without regard to those consequences.
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Externalities enter an agent’s production or utility function
and are chosen by others without regard to the affected
person’s welfare.
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Externalities can be negative but also positive
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Externalities can be consumption or production externalites
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Depletable externalities
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An externality is said to be depletable if the consumption of
the externality by one agent means another does not.
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Many externalities are non-depletable: one person’s
consumption of the externality does not diminish another
agent’s ability to suffer from the externality, i.e. the
externality is non-rival.
Examples:
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Non-depletable: urban congestion, air pollution.
Depletable: dumping waste on your neighbor’s property,
non-allocable acid rain
Externalities have effect for environmental policies, for
healthcare, redistribution and other areas of public sector
economics.
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Externalities and market failures
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Individual choices are taken weighting private costs and
benefits: social cost is ignored.
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Competitive markets yield prices which do not reflect the
social costs (and benefits), only private ones.
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If no external effects exists, social and private costs are equal
and competitive market yield a Pareto-efficient outcome:
when they diverge the result is inefficiency.
Inefficiency comes from
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divergent incentives for economic agents;
creation of increasing returns to scale.
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
The externality problem
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
The externality problem
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If social costs are not considered production is over the social
optimum and a social loss incurs (ABC in figure).
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Note: even at the social optimum the externality is not nil.
Eliminate externality completely is generally not efficient
because it sacrifices other goods which is valuable.
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What are effects on FTWE?
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Divergent incentives
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Suppose there are two individuals (Ann and Bill) and two
goods x cigarettes and y “other goods”.
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Ann smokes, Bill does not but his welfare is affected by Ann
smoking.
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Utility functions are therefore:
U A = U(x A , y A )
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U B = U(x A , y B )
Note: here the externality is negative, hence ∂U B /∂x A < 0
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Divergent incentives
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Pareto efficiency is modified such that:
∂U B /∂x A
MRS A −λ A
= MRT
∂U /∂y A
|
{z
}
externality
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B
A
/∂x
Note: (-λ ∂U
) > 0 (as λ ≥ 0; ∂U B /∂x A < 0;
∂U A /∂y A
∂U A /∂y A > 0):
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hence: MRS + (externality ) = MRT , and MRS is steeper
(larger relative consumption of y A )
how is the MRS wrt the case where no externality exists?
if externality was not considered, what would market
equilibrium be?
Carlo Fiorio
Externalities
(1)
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Non-convexities
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Assume that:
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Total work available (workers×working days) is 1,200 days,
hence:
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we have an upstream chemical firm producing dioxide and a
downstream fish farm.
only factor of production is labor
One day of labor in the farm yields 4,000 fish (f ); one day of
labor in the chemical firm produces 50 tons of oxide (x).
maximum fish produced: 1, 200 × 4, 000 = 4, 800, 000
maximum oxide produced: 1, 200 × 50 = 6, 000
4000
x
MRTxf = MC
MCf = 50
PPF is then: f = 4, 800, 000 −
4,000
50 x
Carlo Fiorio
Externalities
¡
= 4, 000 1, 200 −
1
50 x
¢
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Non-convexities
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Suppose the production of oxide creates a pollutant which
reduces the productivity of the fish farm:
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for every ton of oxide, each unit of labor used in the fish farm
produces 1/2 fish less.
The PPF becomes:
³
x ´
f = (4, 000 − 0, 5x) 1, 200 −
50
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This means that the PPF is convex: the presence of the
externality makes one of the two firms to stop producing
anything (not a Pareto-efficient outcome!)
Carlo Fiorio
Externalities
(2)
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Non-convexities
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
What solutions? The Coase theorem
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The Coase theorem states that bargaining over externalities
will lead to Pareto efficiency, provided property rights are well
defined and no transaction cost exists.
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What is clearly important is the distribution of property rights.
Two main points about externalities:
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in absence of bargaining the outcome is Pareto-inefficient;
if individuals involved do trade, they can continue to bargain
until no Pareto improvement is possible.
Bargaining makes sense when only few individuals are involved
and the externality is depletable. Otherwise, other
mechanisms should be considered for a Pareto-superior result.
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Gov’ts could do better with non-depletable externalities: which
tool do they have?
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
What solutions? The Coase theorem
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
What solutions? Pigou and taxation
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The Pigouvian tax is a tax on production of an externality
designed to bring social and private marginal costs into line.
What are the distributional consequences of this action?
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it depends on what is done with the tax raised.
Polluter would lose and oppose the tax if the tax is given to
agents suffering from pollution or to general taxation.
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Pigou taxation
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Pigou taxation
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For instance, the gov’t could tax the consumption of
sigarettes (x), hence reducing the benefits of smoking more.
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What should the tax t be? Recall (1):
MRS A + externality = MRT
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(3)
Ann will set consumption such that MRS A = (px + tx )/py . In
a competitive system, MRT = MCx /MCy = px /py , which for
Pareto-efficiency means:
px + tx
px
MCx
px
≡
+ externality =
=
py
py
MCy
py
Carlo Fiorio
Externalities
(4)
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
What solutions? Pigou and taxation
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Hence, the tax that leads to efficiency is:
tx
= externality
py
(5)
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Note: this tax is specific to Ann, it must be differentiated at
the individual level for full optimality.
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How would this last analysis change if we were considering an
externality in production? How if the externality was positive?
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
What solutions? Internalization
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Internalization of the externality means that the if the fishery
took over the chemical firm (or viceversa) the merged
company would be forced to take note of the externality if it
wishes to maximize the profits of the joint operation.
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Sometimes internalization is not possible (e.g., externality
from production to consumption)
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
What solutions? Direct control & differential pricing
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Gov’t can set up agencies which fix the amount Q ∗ of optimal
pollution (e.g. closure of city centers because of pollution)
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Direct control is not very easy to implement.
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Direct controls are inferior to pricing when costs differ
between firms and it is not feasible to set controls which
differentiate between firms.
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
tax vs. direct control, w differential cost
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
Choosing the best option
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Typically optimal intervention will depend on the nature of
the externality:
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if externality is depletable or bargaining costs are low : use the
Coase Theorem to find the optimum, defining property rights
and allowing the affected parties to come to an agreement
if externality is non-rival, hence undepletable, then the size of
the externality suggests gov’t intervention (taxes? quantities?)
Although it would be difficult to obtain correct MB and MC
curves, iteration policies could be undertaken and trade of
pollution permits could be undertaken.
Carlo Fiorio
Externalities
Definition
Efficiency condition with externalities
Possible solutions if externalities exist
References
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C&M, Ch. 5 (excluding paragraph 5.4)
Carlo Fiorio
Externalities