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Module 6: Marginal Damage
Functions
- Uses for the Marginal Damage Function
- Estimating Marginal Damage Functions
- Example of Marginal Damage Function Estimates
Traditional cost-benefit analysis is a useful tool in assessing the social desirability of many
programs or projects that impact the environment, but for some decisions other information is
required. Information emerging from cost-benefit analysis is often cast in binary terms. If the
ratio of net benefits to costs is greater than one, the project is a "winner." If the ratio is less than
one, the project should not be undertaken. While this information is appropriate for many
decisions, some decisions require different information. Sometimes policy makers need to
choose a level of a continuous variable, meaning there are an infinite number of choices. The
traditional cost-benefit approach of comparing alternatives breaks down in this case.
For example, for designing and implementing many policies, it is essential to know the
optimal level of pollution or degradation associated with a particular economic activity.
A good example of this is the choice of an environmental standard for effluents entering a river.
It is not enough to say that "some river cleanup" is a socially beneficial endeavor. To maximize
the well-being of citizens, finding the optimal level of cleanup is necessary. In general, this
means determining the economic costs of controlling the pollution and comparing them to the
benefits of improving water quality in the river. The marginal damage function a useful
tool for estimating the benefits that accrue to reductions in levels of pollution.
1. Uses for the Marginal Damage
Function
The marginal damage function relates the per unit change in economic welfare to the per
unit change in a pollutant. Figure 1,
illustrates a possible marginal damage schedule that describes the relationship between increases
in pollution emissions and increases in welfare loss. Conversely, as pollution emissions
decrease, welfare losses to society would likewise decrease. In this case, welfare losses from
initial increases in pollutants are small, but at some point increase rapidly. The shape of this
function is important, because it will be compared to the costs of pollution control. If benefits
from reducing pollution exceed the costs of reducing pollution a smaller level of pollution is
optimal. If costs of reducing pollution exceed benefits, than society would be better off with
somewhat more pollution. The implicit assumption behind this approach is that for many
pollution agents, some positive level of pollution is optimal. This is just another way of saying
that savings from reducing abatement of pollutants that are not highly damaging can be used to
increase abatement of pollutants that are more highly damaging.
To determine the socially optimal level of a pollutant in the environment, one must also
know the marginal abatement cost function (which describes the costs to society per unit of
pollution reduced) in addition to the marginal damage function. The intersection of the two
schedules is depicted below, in Figure 2. In this case, the level E* is
identified as the optimal level of pollution. Basically, figure two illustrates the fact that when
pollution is high, incremental abatement is relatively inexpensive, but the cleaner the
environment, the more expensive it is to achieve further gains. In contrast, small amounts of
most pollutants have little affect on human welfare, but as amounts increase, welfare is
noticeably decreased.
2. Estimating Marginal Damage
Functions
Marginal damage functions are typically estimated through a series of stages.
Conceptually, the system of stages might look as follows, Figure 3. In this particular case, we consider the emission of a pollution that
results in a decrease in the level of environmental quality, but one could measure the damages
associated with changes in land use or any other environmental problem in a similar manner.
The first box in the diagram depicts the emissions of the pollutant. These emissions are dispersed
through the environment by wind, surface water currents, underground movement of water and
other processes and are transformed into other compounds through natural processes and through
chemical reactions with other pollutants. For example, emissions of sulfur dioxide are carried by
wind currents to distant locations, transformed into other substances such as sulfate and sulfuric
acid, and combined with other pollutants to contribute to the acid rain and tropospheric ozone
problems.
The second box represents how these pollutants influence the ambient concentrations of the
pollutant, such as the ground level concentrations of ozone and sulfate particles, or the acidity
levels of alpine lakes.
The third box measures the exposure of living organisms to the pollutant,
or how the pollutant comes in contact with living organisms. Exposure would be measured very
differently for different types of pollution. For example, for sulfate pollution the concentration
of sulfate in the air (measured as parts per million) is used to measure the exposure of people in
the region. In this case, the concentration variable and the exposure variable could be the same,
because behavior does not usually have much of an affect on exposure. However, on the very
worst air pollution days, people might stay inside for longer periods of time, avoid jogging and
other outdoor activities, etc. Consequently, using the concentrations on the worst days of the
year may be a poor measure of exposure.
Exposure then leads to physical changes in the living organism. This is often referred to in
the environmental health and toxicology literature as a dose-response relationship. For example,
researchers have developed dose response relationships that show the relationship between blood
levels of lead in children and IQ. Similarly, dose-response relationships have been estimated for
the impact of aquatic pH on trout populations.
Finally, there is the relationship between changes in physical damages and social welfare.
What is the cost to society of reduced populations of trout, increased incidence of cancer, or
reduced IQ of children? These changes in social welfare can be measured by estimating society's
willingness to pay to avoid the damages or by estimating the change in consumer or producer
surplus caused by the change in the system. Damages are usually measured in dollar terms and a
variety of techniques exist for estimating these values, although there are important problems
associated with estimating certain categories of damages.
It should be noted that the information requirements for estimating marginal damage
functions are quite high, and very few have actually been estimated in the literature. One of the
major problems associated with this is the problem of developing estimates of the change in
social welfare associated with the physical damages. This difficulty is virtually the same as that
faced in estimating benefits and costs for a cost-benefit
analysis.
3. Examples of Marginal Damage Function
Estimates
Two particular studies are worthy of examination by readers interested in additional detail
on this methodology. The first is an extensive study conducted by Oak Ridge National
Laboratory for the Department of Energy and the European Communities on electricity
generation fuel cycles and their related damages. A complete fuel cycle includes the extraction,
transportation, and conversion of a fuel into electricity. In developing their damage function
methodology, the researchers identify and model each of the stages mentioned in the diagram
above: (1) Externalities caused by emissions are estimated; (2) the transport and transformation
of those emissions are estimated to derive changes in concentrations of pollutants; (3) physical
responses to those pollutants by humans, as well as ecological and production indicators are
measured; and finally (4) social values according to willingness to pay estimates are assigned to
the responses in pollution changes. Fuel types considered throughout the study include biomass,
coal, hydroelectric, natural gas, oil, photovoltaic, uranium, and wind. An extensive study on the
estimation of the externalities associated with oil fuel cycles is included.
The second is a study conducted for the Bureau of Business and Economic Research and
the Center for Environmental and Estuarine Studies of the University of Maryland. This study
details the effects of agriculture related leachate and runoff on fish populations in the Chesapeake
Bay region. The damage function estimates include : (1) herbicide emissions; (2) their related
concentration changes; (3) the affects of the pollutant increases on submerged aquatic vegetation;
(4) the results of the vegetation changes on fish populations; (5) and the economic losses
associated with those changes. Welfare changes here, were assessed by estimating consumer and
producer surplus changes associated with commercial and recreational fishing.
In addition to its use as a policy formulation device, the marginal damage function can be
useful as a categorization tool for environmental
problems. Each stage of the marginal damage function can have properties. The properties may
be specific to a particular environmental event or generalizable across many different events, and
can be identified for each event with a brief assessment of the problem at hand. For instance, one
common property is whether the community that is being impacted by an externality is
the same community that houses the economic unit causing the damage. Identifying
these properties and categorizing environmental problems in a new and innovative way may aid
decision makers by allowing them to choose policy approaches which address the
properties bringing on and affecting the problem, as opposed to addressing the problem
and its identifiable manifestations. This type of classification could be particularly useful to
sub-national decision makers who have little time and constrained resources for extensive study
of the problems they face on a day to day basis.
References
Cumberland, John H., and James R. Kahn, "The Estimation of Marginal Damage Functions:
An Assessment of the Information Requirements," Northeast Regional Science Review,
no.12, 1982.
Kahn, James R. "The Economic Damages Resulting from the Depletion of Submerged
Aquatic Vegetation in the Chesapeake Bay," PhD Dissertation, University of Maryland, 1981.
Kahn, James R., "Economic Damage from Herbicide Pollution in Chesapeake Bay," Project
Appraisal, vol. 2, no. 3, Beech Tree Publishing, September 1987.
ORNL and RFF, U.S.-EC Fuel Cycle Study: Background Document to the Approach and
Issues, Report No. 1 on the External Costs and Benefits of Fuel Cycles: A Study by the U.S.
Department of Energy and Commission of European Communities, November 1992,
(ORNL/M-2500).
ORNL and RFF, Estimating Externalities of Oil Fuel Cycles, Report No. 5 on the External
Costs and Benefits of Fuel Cycles: A Study by the U.S. Department of Energy and Commission
of European Communities, August 1996.
Rabl, A., and B. Peuportie, "Impact Pathway Analysis: A Tool for Improving Environmental
Decision Making," Environmental Impact Assessment Review, 1995.
Rosa, Duane R., "Modeling of a Marginal Damage Function for Groundwater
Contamination," University of Oklahoma, working paper, 1985.
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