International environmental economics and policy
Topic II: Theory of externalities
Bruno Lanz
Graduate Institute of International and Development Studies
Reminder I
Pareto optimality as a benchmark: re-allocating resources cannot make one person better off without harming another
First fundamental welfare theorem: Complete and perfectly competitive markets lead to Pareto efficient outcomes
Second fundamental welfare theorem: In a well functionning market any Pareto efficient outcome can be obtained via suitable lump sum income transfers
Reminder II
Main feature of a public good: it is available in equal measure to all consumers
In the presence of a public good, resource allocation determined by market forces is not efficient
Self-interested individuals contribute less than the efficient level
Similarly, in many instances environmental quality is shared by many agents
In general we would expect environmental quality to be under-provided
Roadmap
Externality: definitions and examples
Inefficiencies: Formal treatment
What are preferences for the environment?
An alternative view: Demand and supply of environmental quality
Externalities: Definition 1
Meade’s (1973) general definition:
An external economy (diseconomy) is an event which confers an appreciable benefit (inflicts appreciable damage) on some person(s) who were not fully-consenting parties in reaching the decision(s) which lead directly or indirectly to the even in question
Pecuniary externalities
Example: Discovery of a giant oil field
⇒ Oil prices fall, other owners of oil deposits are worse off
The external effect of the discovery is mediated through the price system, so there’s no net loss
For each owner harmed, buyers gain
Pecuniary externalities induce no inefficiencies (only distributional effects)
Other examples
Externalities: Alternative definitions
Starett’s 1988 definitions
In terms of effect:
An externality exists when agent A’s utility or production function depends directly on real variables chosen by another agent B without particular attention given to the effect on A’s well-being
The emphasis is onrealvariables – direct impact on the utility or production possibility set
In terms of reasons:
An externality is present whenever there is an insufficient incentive for a potential market to be created for some good, and the non-existence of this market leads to a non Pareto-optimal equilibrium
Examples
Production externality Consumption externality
Positive impact on social welfare
R&D:
Discoveries by a firm can be used by other firms and thus benefit society as a whole (not just their own profit)
Education:
Individuals with higher education level will benefit the country as a whole (e.g. FDI, employment level, income) not just their future income prospect
Negative impact on social welfare
Pollution:
Firms producing hazardous gases as a byproduct of their activities will affect the health of nearby residents
Environmental externalities: link with public goods
Private provision of public goods involve a positive consumption externality: everyone benefits from individual’s contribution
Many environmental externalities have an incentive structure that is similar to that of public goods
Example:
Frequent smog in Mexico City is due to unfortunate combinations of geography, weather and vehicle traffic
This affects people with respiratory problems
Efforts to reduce smog in the city would benefit these same people, regardless of their contribution to the control effort
In this sense air pollution is a public bad, and a reduction in air pollution is a public good
Externalities: Formal treatment
Consider again an economy with:Two individualsi= 1,2
Two goodsx andz
One factor (labor,l) supplied inelastically
The production ofx causes emissions E
Preferences are represented by a utility function Ui(xi,zi,E) for i = 1,2, with∂U(·)/∂E <0
Production technology forx is written as x =f(lx,E), with ∂f( ·)
∂lx >0,
∂f(·)
∂E >0
Emissions are treated as an input, implying that reducing pollution reduces the output of x by decreasing a productive factor
Production of the clean good is given by z =g(lz), with ∂∂gl(z·) >0
Excursus: What are preferences for the environment?
Two opposing views on individual preferences towards environmental protection
1. Biocentrism: Places the biological world at the center of the value system (intrinsic value of the environment)
2. Anthropocentrism: The environment has value only insofar as it provides material gratification to humans (instrumental value)
Indifference curves?
Note: Utilitarism emphasizes the well-being that people derive from the environment, whatever the source (material or spiritual,
instrumental or intrinsic)
Alternative view: Supply and demand
Market equilibrium:
Consumers maximize utility given prices and income (demand function) Firms maximize profits given prices – in the long run equilibrium zero profit (supply function)
Markets clear
The demand reveals the marginal willingness to pay (MWTP) for an additional unit of the good
The supply is the marginal production cost The market equilibrium is Pareto optimal
Maximize total surplus
Supply and demand for bads
Framing the same problem differently: The supply and demand of bads
Consider that the production of goodx produces ‘garbage’ (or pollution, or emissions) as a byproduct
To accept that the firm stores this garbage in your garden you’d require compensation: The price of garbage is negative
Supply curve: As the price of garbage approaches zero, the profit-maximization point on the production possibility frontier involves more garbage
Demand: At high garbage prices (i.e. near zero), garbage consumption is low
Comparing environmental damages and abatement costs
Determining the efficient level of pollution requires comparing the demand and supply of emissions
Consider an area where J polluting firms and I affected households are located
Firms are coal burning electricity generators selling power on a national market
Households buy power on the national market
Total emissions are denotedE =PJ
j=1ej
Assume all firms contribute uniformly to total emissions in the area
Demand for emissions reduction: Damage function
Aim: Derive a simple function that summarizes the disutility associated with emissions in monetary units
Describes the MWTP for emissions reduction
Assume households have utility functionUi(yi,E) =yi −Di(E) where yi is income andDi(E) is the disutility caused by pollution
Note: Preferences are quasi-linear in income, and the marginal utility of income is one
⇒ Di(E) can be interpreted as the dollar value of lost utility
We further assumeDi0(E)>0 and Di00(E)≥0
The aggregate damage function is D(E) =PI
i=1Di(E)
Abatement costs
Assume that the cost associated with electricity generation is separable from those required to reduce emissions below initial level Define the cost of pollution reduction, orabatement cost function, as Cj(ej)
If the firm can freely chose it’s emission level we haveCj(ej) = 0 Forej <ej thenCj(ej)>0, with C
0
j(ej)≤0
A marginalreductionin emissions increases the marginal abatement cost, so the marginal abatement cost function is:
MACj(ej) =−C 0
j(ej)≥0, ej <ej
We also assume that the marginal abatement cost increases when emissions are reduced (weakly convex): MAC0j(ej)≤0, ej <ej
Efficient allocation
Emissions harm consumers, and emissions control has an opportunity cost to firms
Efficient outcome: balance the two costs to the economy, i.e. minimize the total cost of the externality to society
The social objective function is:
SC(e1, ...,eJ) = J
X
j=1
Cj(ej) +D(E)
FOC w.r.t. ej:
−Cj0(ej) =D
0 (E)
which also implies Cj0(ej) =C 0
Property rights and the Coase theorem (1960)
For some classes of environmental problems, public intervention may not be necessary to restore efficiency
If property rights are clearly defined, and individuals value these rights, they can enter a bargaining game to improve the final outcome
Akin to Pareto-improving, voluntary trade
Coase theorem: Negotiations over private contracts between rational agents will lead to an efficient pollution level
As for our treatment of Pareto allocations, the initial assignment of property rights does not matter for efficiency (invariance claim)
Coase Theorem: Bargaining game
Assume I=1 and J=1, so that
1. All damagesD(E) are borne by the affected household
2. All pollution is from emissions by the firm (e1=E)
Negotiation: One party can suggest a contract (E,p), where a pollution level E is tolerated in exchange for a transfer paymentp In such negotiation, the party who does not own the property rights has to bears transaction costsT
It must seek out the other party and formulate an offer in order to start negotiating
We assume that both players are fully informed about preferences and technology, and solve the sequential game for a sub-game perfect equilibrium
Households hold property rights
When pollution rights are assigned to the affected household, it has the legal right to zero emissions
However the firm may seek to engage the households into a
negotiation: household may accept payment from the firm in exchange for allowing a non-zero level of pollution
In such negotiation, the firm bears transaction costs T
Since the household will refuse any contract for whichp <D(E), equilibrium behavior requires the firm to chose p=D(E)
Just compensate the household for the damage suffered
The firms’s total cost isTC(E) =C(E) +D(E) +T
FOC:−C0(E) =D0(E)
The condition T ≤C(0)−[C(E) +D(E)] must also hold for the gains of the negotiation to be positive
Firms hold property rights
If the firm is endowed with the pollution right, the household can suggest a contract under which the firm will reduce pollution in exchange for compensation
The transfer payment should just compensate the firm for the abatement costs incurred (p=C(E))
The household will chose E to maximize
y−[D(E) +C(E) +T]
FOC:−C0(E) =D0(E)
Assumptions required for the Coase theorem to hold
Individual bargaining simplifies the information problems because individuals are usually better informed than the government Assumptions underlying the Coase theorem:
Agents behave in an optimizing manner
Small transaction costs (costless enforcement)
Perfect information
Typical failures of the Coase theorem
Asymmetric information: revelation problem (exaggerate / expose to obtain compensation)
When many parties are involved (public goods), difficult to define property rights, and magnifies problems of cooperation (e.g. holdouts)
Non-representation of some parties: space / time may separate the polluters and the victims, hence the outcome of negotiations is not socially optimal
Invariance claim: Prior distribution of property rights will affect the wealth of parties as the property rights have value
This implies different demand through income effects
Should households be compensated for damages?
Polluter pays principle: the entity producing emissions is responsible for bearing the cost of pollution preventionandcompensating victims for the damages incurred
In our framework, this means giving the property rights to the households
And compensating them according to the value of the remaining level of emissions
If households have some control over the damages they suffer, then ex-post compensation will introduce inefficiencies
For example, people who experience respiratory problems on days with poor air quality can adjust their schedule to minimize outdoor time
Socially optimal avertive behavior
The damage function for the household isD(E,x), wherex is a private good mitigating mitigating the negative effect of pollution
The consumption ofx yields no utility per se
Assume ∂D/∂x <0 and ∂2D/∂E∂x<0
Increasingx causes both total and marginal damages to fall
Efficiency condition: minE,x{D(E,x) +pxx+C(E)}
FOCs: −C0(E) =∂D(E,x)/∂E and−∂D(E,x)/∂x =px
Avertive behavior and compensation
Assume that the firm must fully compensate ex-post external damages By definition, the household suffers no adverse consequences from the externality (he is compensated)
There is no incentive to spend private resources: x= 0
The firm’s task is to chose E that minimizes abatement and compensation to the household
minE{C(E) +D(E,0)}
FOC:−C0(E) =∂D(E,0)/∂E This is not efficient
