The first welfare theorem: in an economy in which

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Topic 2 Externalities

• The first welfare theorem in an economy in which
• all agent are price-takers
• there are no externalities
• there are no scale economies
• information is symmetric between buyers and
  sellers
• market allocations are Pareto efficient.
• Recall our definition of Pareto efficiency
• An outcome is Pareto efficient if it is
  impossible to come up with an alternative outcome
  in which at least one person can be made better
  off without any one person being made worse off.

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Topic 2 Externalities

• Related terminology a reallocation constitutes a
  Pareto improvement if it makes at least one
  individual better off and no individual worse
  off.
• Typically such reallocations are not possible. In
  almost any reallocation will be winners and
  losers.
• A reallocation is a potential Pareto improvement
  (PPI) if the winners could in principle
  compensate the losers and still be better-off.
• Thus, a reallocation is a PPI if the gains to the
  winners more than offset the losses to the
  losers.
• Such a reallocation is said to increase social
  surplus.
• Note that there is no requirement in the
  definition of PPI that the winners actually
  compensate the losers.
• The PPI criterion will be equivalent to the
  surplus maximization criterion.

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Topic 2 Externalities

• An externality (or external effect) is a cost or
  benefit associated with an action that is
  external to the agent taking that action.
• Externalities can be positive (an external
  benefit) or negative (an external cost).
• The archetypal negative externality is unpriced
  pollution
• An action generates pollution and that pollution
  has an effect on other agents for which the
  polluting agent does not have to account.
• If an action has an associated externality then
  the privately optimal action may be inefficient
  from a social perspective.

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Topic 2 Externalities

• Private optimum
• Let PB(z) denote private benefit as a function of
  some action z (eg. benefit from driving a car z
  kilometers).
• Let PC(z) denote the private cost of z (eg. fuel
  and maintenance costs).
• An agent will choose a level of z that maximizes
  her private surplus (or private net benefit)
• PB(z) - PC(z)
• Under reasonable assumptions, we can often define
  the private optimum by z
• MPB(z) MPC(z)
• where MPB denotes marginal private benefit and
  MPC denotes marginal private cost.

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Topic 2 Externalities

MPC

• Private Optimum is given by allocation z

MPB
z
z

• If all assumptions from the first welfare theorem
  hold, this will also be the social optimum.

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Topic 2 Externalities

• Social optimum
• Suppose action z imposes an external cost D(z)
  and an external benefit G(z).
• Define the social cost of z
• SC(z) PC(z) DG(z)
• and the social benefit of z
• SB(z) PB(z) G(z)
• The social optimum maximizes social surplus
• SB(z) - SC(z)
• Under reasonable assumptions we can often define
  the social optimum by z
• MSB(z) MSC(z)
• where MSB denotes marginal social benefit and MSC
  denotes marginal social cost.

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Topic 2 Externalities

• A positive externality
• That is G(z)gt0, for simplicity assume D(z)0.
• The difference between MSB and MPB is called
  marginal external benefit (MEB)
• The presence of the external benefit means z lt
  z
• ie. the privately optimal level of activity is
  lower than the socially optimal level.
• Intuition the agent does not take into account
  the external benefit she bestows on others when
  she chooses her action, and so her chosen level
  of the action is too low from a social
  perspective.

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Topic 2 Externalities
Topic 2 Externalities

• Note that a forced reallocation from z to z
  would make the external agents better off but
  would make the source agent worse off.

MPCMSC
b
c
a
d
MSB
z
MPB
z z

• Thus, the reallocation would not be a Pareto
  improvement.

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Topic 2 Externalities
Topic 2 Externalities

• Gain to external agents area (abcd)
• Loss to source agent area (acd)
• The gain to the external agents is greater than
  the loss to the source agent.

MPCMSC
b
c
a
d
MSB
z
MPB
z z

• The reallocation from z to z would be a
  potential Pareto improvement, since external
  agents could compensate the source agent for her
  loss and still be better off.
• Social surplus would increase by area (abc).

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Topic 2 Externalities

• A negative externality
• That is D(z)gt0, for simplicity assume G(z)0.
• The difference between MSC and MPC is called
  marginal external cost (MEC)
• The presence of the external costs means z gt z
• ie. the privately optimal level of activity is
  higher than the socially optimal level.
• The level of activity is too high from a social
  perspective. The agent does not take into
  account the external cost she bestows on others
  when she chooses her action.

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Topic 2 Externalities
Topic 2 Externalities
MSC

• Note that a forced reallocation from z to z
  would make the external agents better off but
  would make the source agent worse off.

MPC
c
b
d
a
MPBMSB
z
z z

• Thus, the reallocation would not be a Pareto
  improvement.

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Topic 2 Externalities
Topic 2 Externalities
MSC

• Gain to external agents (reduced external cost)
  area (abcd)
• Loss to source agent (foregone private surplus)
  area (abd)
• The gain to the external agents is greater than
  the loss to the source agent.

MPC
c
b
d
a
MPBMSB
z
z z

• The reallocation from z to z would be a
  potential Pareto improvement, since external
  agents could compensate the source agent for her
  loss and still be better off.
• Social surplus would increase by area (bcd).

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Topic 2 Externalities

• Some important examples of externalities
• Open Access Resources
• A resource to which many agents have access to.
• Example unregulated fisheries
• When one agent harvests fish, she draws down the
  stock of the resource, she does not take into
  account the cost she imposes on other agents in
  terms of reduced fishing productivity.
• Each agent engages in harvesting effort up to the
  point where MPCMPB but since MSC gt MPC, each
  agent harvests too much from an efficiency
  perspective.

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Topic 2 Externalities

• This behaviour can lead to the depletion of the
  resource.
• Such an outcome is sometimes referred to as the
  tragedy of the commons.
• In principle the problem can be solved through
  the assignment of property rights (as with
  fishing licenses and timber licenses), but
  transaction costs (and fairness issues) often
  call for direct government intervention.

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Topic 2 Externalities

• b) Public goods
• Public goods are characterized by two features
• joint consumption possibilities can be enjoyed
  by more than one agent simultaneously
• high exclusion costs is very costly to prevent
  agents from consuming the good
• Public goods are a kind of positive externality
  the provision of the good by one agent bestows a
  positive benefit on other agents.
• The market provision of public goods (or more
  generally, the provision of public goods in
  private equilibria) tends to be inefficient.
• Why? MSBgtMPB, and the external benefit cannot be
  priced because the good is non-excludable.
• Each agent has the possibility of free-riding
  (that is, not paying ) once the good has been
  provided.

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Topic 2 Externalities

• If two agents can potentially be better-off at
  some allocation than at the existing allocation ,
  why dont the agents themselves agree to a
  reallocation?
• Where is the need for government intervention?
• The so-called Chicago view is that there is no
  role for government intervention except to assign
  and enforce property rights.
• Why might the market not realize such gains even
  if property rights are assigned?
• The problem is transaction costs (Coase 1960).
• The cost of negotiating an agreement can more
  than offset the gains from the agreement that
  is, the process of moving from one allocation to
  another is itself costly.

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Topic 2 Externalities

• The role for government intervention on
  efficiency grounds rests on the possibility in
  some circumstances - of institutional advantage
  over the market.
• That is, in some cases government intervention
  may be able to achieve an efficiency-enhancing
  reallocation at lower transaction costs than the
  market (eg. global climate change agreements).
• The mere existence of externalities, and their
  adverse implications for the environment, is not
  enough to justify government intervention.
• Any proposed government intervention on
  efficiency grounds should be subject to the
  question can the government do better than the
  market?
• In many aspects of environmental policy, the case
  for intervention is compelling.