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Economics of Environmental Policy Instrument DesignLecture 1: Review of public goods, externalities
Pareto optimality
When a reallocation of resources cannot make at least one person better off without making
someone else worse off.
- Doesn’t say anything about the allocation
- X inside frontier so Pareto improvement possible
- On frontier makes it optimal
Markets and Pareto optimality
- Self-interested party can trade to make himself better off (else they would not trade)
- First Welfare Theorem: competitive equilibrium is Pareto efficient
- When does a market outcome not achieve Pareto efficiency?
o Externalities
o Market power
o Public goods
o Asymmetric information
Market failures: conditions under which free market does not lead to efficient outcomes.
Imperfections:
- Transaction costs, barriers
- Imperfect competition
o Increasing returns to scale
- Imperfect information
- Behavioral failures
Missing markets:
- Externalities
- Public goods
- Poorly defined or undefined property rights
- Asymmetric information
One of the reasons why environmental policy is needed is because of market and policy failures.
These are interlinked with the evolution of property rights.
Externalities
Benefits or costs from an action that accrue to a third party and that are not reflected in market
prices for the acting parties.
Negative: agent A’s activity causes a damage or imposes a cost to agent B.
Positive: agent A’s activity causes a benefit to agent B.
Both are problematic from a social perspective.
1
,Examples of negative externalities
- Industrial pollution
- Noise from vehicles
- Smoking (second hand smoke)
- Distribution of GMOs (or accompanying herbicides) to adjacent organic fields
- Fishing a limited fish stock
Result: there are ‘too much’ of these activities (because these costs are not taken into account).
Examples of positive externalities
- A neighbor paints her house
- Picking up waste from the streets
- Charity (you benefit because other people donate)
- Education
- Spillovers from research
- Vaccination (herd immunity)
Result: there are ‘too little’ of these activities.
Modeling externalities
- Two individuals receive utility from 2 private goods X and Z, and disutility from emissions E
- Utility functions:
o U1(x1,E)+z1
o U2(x2,E)+z2
- A single firm produces X using emissions as an input
o Production function X = f(E)
o The more individuals want to consume x rather than z, the more emissions involved
- The economy is constrained so that X = x 1 + x2 and Z = z1 + z2
o Disutility from emissions: z1 and z2
o Note that the later constraint implies z2 = Z – z1
Pareto problem
Maximize utility for person 1 subject to meeting a reference utility for person 2 and the technology
and scarcity constraints.
- Lagrangian: constrained optimization
- Constraint: gamma γ = shadow cost of output
- Constraint: lambda λ = shadow cost of maintaining 2’s utility
- Gamma γ and lambda λ are shadow values
- What’s between bricks is the constraint
- U with bar is something like a threshold
- Then: FOC
- First derivative of Lagrangian / marginal utility of another unit of consumption of x 1 for
individual 1 EQUALS the shadow cost of output (γ)
Characterization of the Pareto optimum
- Marginal utility of x is equalized at the shadow value
2
, - Marginal rate of substitution (marginal cost in utility terms) of emissions equals the marginal
product of emissions
∂U 1 (∙) ∂ U 1 (∙) ∂ U 2 (∙)
=
∂ x1 ∂E ∂E
– – =
∂U 2 (∙) ∂ U 1 (∙) ∂ U 2 (∙)
=γ
∂ x2 ∂ x1 ∂ x2
f’(E)
Decentralized market problem
Individuals maximize utility, taking p (competitive price of X), incomes y 1 and y2, and E as given:
maxU1(x1,E) + (y1 – px1)
maxU2(x2,E) + (y2 – px2)
Individual’s first-order conditions:
∂U 1 (∙)
X1: =p
∂ x1
∂U 2 (∙)
X2: =p
∂ x2
Market problem (2)
- Firms maximize profit, taking p and technology as given: max pf(E)
- Firm’s first-order condition E: pf’(E)=0
- Remember individual conditions:
∂U 1 (∙)
o X1: =p
∂ x1
∂U 2 (∙)
o X2: =p
∂ x2
- Characterization of market solution
∂U 1 (∙) ∂U 2 (∙)
o Marginal utility of x is equalized: =
∂ x1 ∂ x2
o Marginal product of emissions equals 0: f’(E) = 0
Market failure
Optimal Decentralized market
Emissions have a shadow cost Emissions are free
∂U 1 (∙) ∂U 2 (∙) ∂U 1 (∙) ∂U 2 (∙)
= =γ =
∂ x1 ∂ x2 ∂ x1 ∂ x2
∂ U 1 (∙) ∂ U 2 (∙) f’(E) = 0
∂E ∂E
– – = f’(E)
∂ U 1 (∙) ∂ U 2 (∙)
∂ x1 ∂ x2
Firms take prices as given, so it uses emissions as long as it makes sense to the firm. This is how you
get market failure. We want the firm to take into account emissions E.
What the market wants to do and what is optimal doesn’t look that different
The market just takes into account prices more?
You want the right incentives for E for the market
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, So let the firms pay for E emissions taxes
‘Internalizing’ market failure
- Get the incentives to line up
- Make the firm pay tax τ for the utility cost
- Firm will maximize: max pf(E) – τE
- New first-order condition E: pf’(E) = τ
- Possible value for τ:
Public good
A good for which the consumption by one individual does not reduce the amount available to be
consumed by another individual.
- Non rival: my consumption doesn’t affect availability
- Non excludable: no one is excluded from consuming the good
Examples: public parks, dikes, defense
Free-rider problem
When those who benefit from a good or service do not pay for them, which results in an
underprovision of those goods or services. This is the non-excludable goods problem.
Since consumers share in consumption, each consumer has an incentive to rely on others to make
purchases of the public good. Leads to inefficiency.
Private versus public goods
Private goods are:
- Excludable: if you don’t pay you won’t get the good
- Rival: if you consume a certain amount of the good, there is less to consume for others
Public goods are:
- Non-excludable: if you don’t pay you can still get the good
- Non-rival: your consumption of the good does not diminish the amount available for others
Club goods: these goods are non-rival but excludable (e.g. cable or satellite TV, websites).
Common property goods: non-excludable but rival (e.g. fisheries, well water, other open access
resources).
Impure public goods
Goods occupying the middle ground between these extremes: i.e., exhibit some excludability or
rivalness. Examples:
- Roads: costly to exclude people (given current technology) but as more and more people use
it consumption becomes rival (congested)
- Polar bears: rival when hunted; congestible when viewed in person; non-rival and non-
excludable when enjoyed for pure existence value (i.e. when people get utility from knowing
polar bears exist even though they can’t see them in person)
Matrix of public and private goods
Rivalrous Non-rivalrous
Excludable Private good Club good
Non-excludable Common property resource Public good
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