EPA-600/5-76-002
May 1976
Socioeconomic Environmental Studies Series
1C WELFARE IMPACTS OF URBAN NOISE
Office of Health and Ecological Effect!
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application of
environmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the SOCIOECONOMIC ENVIRONMENTAL
STUDIES series. This series includes research on environmental management,
economic analysis, ecological impacts, comprehensive planning and forecast-
ing, and analysis methodologies Included are tools for determining varying
impacts of alternative policies; analyses of environmental planning techniques at
the regional, state, and local levels; and approaches to measuring environmental
quality perceptions, as well as analysis of ecological and economic impacts of
environmental protection measures. Such topics as urban form, industrial mix,
growth policies, control, and organizational structure are discussed in terms of
optimal environmental performance. These interdisciplinary studies and systems
analyses are presented in forms varying from quantitative relational analyses to
management and policy-oriented reports.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161,
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EPA-600/5-76-002
May 1976
ECONOMIC WELFARE IMPACTS OF URBAN NOISE
by
Rodney Thorpe
Thomas Holmes
QEI, Inc.
Bedford, Massachusetts 07130
Contract No. 68-01-2634
Project Officer
Dennis Tihansky
Washington Environmental Research Center
Washington, D.C. 20460
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
OFFICE OF HEALTH AND ECOLOGICAL EFFECTS
WASHINGTON, D.C. 20460
EPA-RTF LIBRARY
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DISCLAIMER
This report has been reviewed by the Office of Health and Ecolog-
ical Effects, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U.S. Environmental Protection
Agency, nor does mention of trade names or commercial products consti-
tute endorsement or recommendation for use.
11
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ABSTRACT
The basic purpose of this project was to develop a con-
ceptual framework for estimating the social welfare gains or
benefits of reducing current noise levels in urban environments.
The project has concentrated on developing economic welfare
theory and empirical techniques to assess willingness-to-pay by
individuals for noise avoidance. Particular attention was paid
to noise produced by motor vehicles and noise produced by
operations at construction sites. Noise pollution produced at
airports and by aircraft was purposely de-emphasized in this study.
The theoretical effect of the localized nature of noise
on people's willingness-to-pay to control noise was investigated
and found to be important. The theoretical effect of noise
averting activities on people's willingness-to-pay to control noise
was also found to be significant. An efficient pricing scheme
for aggregate noise disturbance was devised, based on people's
willingness-to-pay for noise reduction. A systematic analysis
of the case of many suppliers of the public good of noise
reduction was carried out.
A questionnaire was developed to elicit responses on the
physical and psychic costs of noise in urban areas. This
questionnaire will attempt to assign dollar values to the costs
of noise pollution by determining people's wi'llingness-to-pay
to control or reduce noise.
m
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TABLE OF CONTENTS
PAGE
I. INTRODUCTION 1
II. WILLINGNESS-TO-PAY AS AN EFFICIENCY GUIDE FOR THE
REGULATION OF NOISE DISTURBANCE 6
by Richard Zeckhauser
A. The Characteristics of Noise and Government Regulation 8
B. Consumer Valuation 22
C. Defining the Efficient Outcome 34
D. Implications and Conclusions 68
III. THE PRICING OF AGGREGATE NOISE DISTURBANCE 75
by Thomas Holmes
A. Location Specific and Periodic Properties of Noise 77
B. The Many Sources of Noise and Stochastic Measures 80
C. Public Goods, Market Failure and Externalities 88
D. Consumers' Rights and Public Factors of Production 93
E. A Theorem on the Pricing of Aggregate Noise Disturbance 97
F. Proofs of the Price Theorem and its Corollary 108
G. Interpretation of the Price Theorem 116
H. Conclusion 132
IV. DISCUSSION OF THE QEI QUESTIONNAIRE ON NOISE POLLUTION 134
by Rodney Thorpe
A. Introduction
B. General Questions on Attitudes Toward Noise 149
C. Questions on Willingness-to-Pay for Noise Reduction 155
D. Questions on Respondent Characteristics 158
E. General Information on the Respondent. 159
V. DESCRIPTION OF THE PRETESTING OF THE QEI NOISE POLLUTION
QUESTIONNAIRE AND DISCUSSION OF RESULTS 162
by Rodney Thorpe
A. Selection of the Sample for the Pretest 162
B. Selected Results of the Pretest 163
C. Selection of the Sample to be Interviewed in the
Actual Test 179
APPENDIX - BIBLIOGRAPHY 183
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SUMMARY
Willingness-to-pay for the regulation of noise disturbance was
investigated and found to be a valid and determinable indicator of
people's annoyance with noise. The economic effects of the fact
that noise is a very localized phenomenon were also investigated and
found to be very important. A pricing scheme for aggregate noise
disturbance was devised, based on people's willingness-to-pay for
noise reduction. This derivation indicates that with respect to
Pareto efficiency it makes no difference whether the public is
compensated for damage due to noise or the producers of the noise
are taxed. An attitudinal survey was developed to determine people's
willingness-to-pay for specific reductions in overall noise level.
This questionnaire was pretested and found to be a valid instrument
for determining people's willingness-to-pay for noise reduction.
The results of the pretest were also used to determine the size of
the sample for the actual test, the seasonal period of sampling, and
the distributional characteristics of the population to be sampled.
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RECOMMENDATIONS AxND CONCLUSIONS
Our principal recommendation is that the questionnaire on
noise, that we devised and pretested, be administered to a sample
chosen according to the rules we developed. We believe that certain
modifications should be made in certain of the questions in the
survey, but that these modifications are basically rather minor.
Following the administration of the questionnaire to the sample
chosen, we recommend that the results of the survey be analyzed
extensively by several different techniques, including regression
analysis and possibly principal components analysis or discriminant
analysis.
Our principal conclusions are the following:
1. Willingness-to-pay for the regulation of noise
disturbance is a valid and determinable indicator
of people's degree of annoyance with noise;
2. A questionnaire is a valid instrument for determining
people's willingness-to-pay for specific reductions
in overall noise level; and
3. The determination of willingness-to-pay for noise
reduction by the public is essential for setting ef-
ficient and effective standards for noise control.
Vll
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ACKNOWLEDGEMENTS
This project was conducted under an E.P.A. grant to
Q.E.I., Inc., 119 The Great Road, Bedford, Massachusetts,
01730. Both Rodney Thorpe and Thomas Holmes were employees
of Q.E.I.,Inc. during the entire course of this project.
Richard Zeckhauser was a consultant to Q.E.I., Inc. for
this project.
The support of-the Environmental Protection Agency, and
the assistance provided us by Dr. Dennis Tihansky of E.P.A.'s
Washington Environmental Research Center, is gratefully
appreciated.
All errors of fact and faults of judgment and omission
are the authors' responsiblity.
viu
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CHAPTER I
INTRODUCTION
This report represents QEI's Final Report to the Environ-
mental Protection Agency on Contract No. 68-01-2634 entitled "Econo-
mic Welfare Impacts of Urban Noise." The purpose of this contract
is to develop a conceptual framework for estimating all social wel-
fare gains or willingness-to-pay indicators for reducing current
levels of noise in urban areas. In order to perform this study two
main areas were investigated. First, an economic welfare theory
and empirical techniques to assess individual willingness-to-pay for
noise avoidance or reduction were developed. Second, a questionnaire
was designed to elicit responses from individuals on the psychic costs
of noise in urban environments. This questionnaire was then pretested
on a sample of people drawn from the Boston metropolitan area.
Noise is defined to be unwanted sound. Noise is, in large part,
a subjective phenomenon relating to the reactions of people to cer-
tain types of physical sound. Noise may well have adverse effects
on the physical, mental, and emotional health of some members of the
public, but the form of the relationship between noise and health is
unknown. However, noise certainly is the cause of much irritation
and annoyance to a large part of the public. The degree of annoyance
caused members of the public is, of course, subjective and varies
from person to person.
In economic terms, noise is considered to be an externality,
produced as an unintentional, but usually unavoidable, by-product
during the production of some other good or service, such as the
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provision of transportation services. The production of noise as
an externality is usually unintentional and not particulary desired
by the producers. The benefit of noise to the producers is usually
zero, but the cost of noise to the public is larger than zero. How-
ever, it would certainly cost many of the producers of noise large
sums of money to reduce the noise produced by them as a by-product.
The question arises as to who should bear this additional production
cost for reducing the noise produced. Either the producers or con-
sumers must bear this cost, and it seems clear that ultimately the
consumers will bear virtually the entire cost of noise reduction
through higher prices on consumer products. Thus, it seems essential
to determine how much the public is willing to pay for noise reduction.
It should be noted that the free competitive market can not
handle the situation that arises due to the effects of noise or
any other externality. This is because noise is, in part at least,
a so-called public good. For a moderate expenditure, few can totally
isolate themselves from the effects of noise. Also, what one person
does to protect himself from the effects of noise in no way protects
anyone else from its effects. Thus, it seems clear that the govern-
ment must intervene to protect most of the members of the public from
the effects of noise. But, in situations such as this, the government
must be seen as acting fairly and equitably toward all concerned.
Noise is, of course, similar in many of its effects to other
externalities such as water or air pollution. However, in certain
important respects noise differs markedly in its effects from water
or air pollution. These differences necessitate a somewhat different
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analysis and treatment of noise pollution from that of air or
water pollution. The following paragraphs present a discussion of
some of the most important differences between noise pollution and
air or water pollution.
First, noise is a very localized phenomenon affecting individuals
almost solely. Noise produced at a certain location can only be
heard by, and will only have an effect on people within a certain
distance of the location of the noise source, since the intensity of
noise diminishes rapidly with the distance from its source of pro-
duction. This suggests that the regulation and control of noise
pollution should be on a local basis or should proceed on an area-by-
area basis. Since all the noise that affects a certain area is pro-
duced in or near that area, regulation and reduction of noise could
certainly be accomplished on an area-by-area basis (unlike air pol-
lution which can be transported substantial distances from its source
of production). The fact that noise is a local phenomenon also implies
that people have additional options in avoiding noise around their
residences say, i.e., they can change their place of residence to some
quieter location or they can plan to be absent from their residences
during the noisiest times of the day.
Second, noise ceases to exist almost as soon as it has been
produced, unlike air pollution. This implies that for a noise to
exist continuously over a period of time it must be continuously
produced by the source. Thus, two very different types of noise are
possible, noises that last a very short time, like the sound of a
pistol shot, and noises that remain at approximately the same intensity
for a period of time, such as that produced by a truck traveling at
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constant speed. Thus, there is a tremendous variation in the noise
intensity level over time, implying that standards or regulations for
noise control must consider both the average intensity level of noise
(during a typical day) and the maximum noise intensity level attained.
Both the intensity peaks of noise and the average levels must be con-
sidered in any policy of control. This variation in noise level during
any period of a day or more also raises the possibility of imposing
different standards for different parts of the day, say requiring
substantially lower maximum noise levels at night when people are more
liable to be disturbed.
Third, the degree or extent of the effects of noise on people's
physical, mental or emotional health have not been definitiely deter-
mined except in a few extreme cases. Thus, using the effects of noise
on health as a means for setting noise regulations seems to be pre-
cluded. The principal effects of noise on people appear to be through
the annoyance or irritation caused them. However, degree of annoyance
or irritation is very difficult to assess precisely, implying that
setting of noise regulations or standards on the basis of degree of
public annoyance will also be rather difficult. Also, noise appears
to affect different people differently; some persons seem to be far
more sensitive to noise of a certain level than are others. This wide
variation in individual sensitivity to noise makes an assessment of
the annoyance or damage caused by a certain level of noise even more
difficult.
Fourth, it is fairly easy for many people to do much to shield
themselves from the adverse effects of noise pollution, unlike air pol-
lution, from which it is hard to protect oneself. People can purchase
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air conditioners or double-pane glass for their windows, and thus
protect themselves from a fairly high degree of noise. People can
also avoid noise by staying away from their homes during particularly
noisy periods. But such purchases or actions will only reduce the
effect of noise pollution on the purchaser; usually no one else will
obtain any benefits from such a purchase. However, probably the
government should set noise regulations which will benefit everyone.
But, those who have already purchased such noise-reducing devices or
those who have taken steps to avoid noise will certainly receive less
benefit from such regulations and will therefore be less willing to
pay part of the costs for establishing such regulations.
To perform this study we were required to accomplish the five
tasks listed in the Statement of Work for this contract. Task A -
a literature review on the economic welfare impacts of noise pollution -
resulted in the annotated bibliography which comprises the Reference
Section of this report. Task B - development of an economic welfare
theory and empirical techniques to assess willingness-to-pay by individ-
uals for noise avoidance or reduction - resulted in Chapter II of this
report, written by Dr. Richard Zeckhauser consulting for QEI and in
Chapter III. Task C - designing a questionnaire to elicit responses
on the psychic costs of noise in urban areas - resulted in the
questionnaire presented in Figure 4.1 and the discussion given in
Chapter IV. Task D - pretesting the questionnaire on a sample of
people drawn from the Boston metropolitan area - and Task E - using
the results of this pretest to derive a procedure for selecting the
sample of persons to be tested with the final version of the question-
naire, such procedure to include the size of the sample, the seasonal
period or duration of sampling, and the distributional characteristics
of the population - resulted in the discussion presented in Chapter V.
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CHAPTER II
WILLINGNESS-TO-PAY AS AN EFFICIENCY GUIDE FOR THE
REGULATION OF NOISE DISTURBANCE
by Richard Zeckhauser
Introduction
Noise is an economic commodity. Its presence as a disturbing
factor affects the welfare of individuals. In this regard it is no
different than food, health, or television sets. The physical pro-
perties of noise are such that no market can exist so that the dis-
turbance it produces can be bought and sold in the manner of apples
and pears. One consequence of this inability to conduct market trans-
actions is that the government may wish to play a regulatory role in
determining what sorts of noise disturbances are generated in which
locations.
If the government is to intervene in this manner, it will have
to have information on what noise disturbance or its absence is worth
to individuals. The purpose of this essay is to provide a framework
suggesting what information is appropriate to gather for this purpose,
and to detail the manner in which it could be profitably employed.
The Characteristics of Noise and Government Regulation section
describes the market failures associated with noise, details some key
characteristics of noise as a commodity, and then describes some
special characteristics relating total noise disturbance to the noise
outputs of different producers.
The section entitled Consumer Valuation discusses difficulties
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in determining consumers' valuations of noise disturbances. It
lays out the methodology supporting the willingness-to-pay approach,
and presents as well some of the principal arguments for alternative
frameworks.
The third section of the essay describes the way consumer valu-
ations should be employed when Defining the Efficient Outcome. Three
major methodological considerations are set forth which must be ex-
plicitly considered when defining efficient levels for noise dis-
turbance.
1. Possibilities for noise averting activities must be ex-
plicitly recognized when making willingness-to-pay determinations.
2. Since noise disturbance is a local phenomena, and since
individuals can shift locations in response to changes in noise levels,
a general equilibrium model should be employed to determine the value
of noise reductions in particular locations.
3. The determination of efficient noise levels should recognize
the costs of changing present patterns of noise levels and averting
behaviors.
The concluding section of this essay traces the implications of
the analysis for different noise valuation procedures, and then pro-
vides a more summary conclusion.
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A- THE CHARACTERISTICS OF NOISE AND GOVERNMENT REGULATION
1. /^Catalogue of Market Failures Associated with Noise
The first question to be considered when evaluating the possibility
of government intervention to regulate the generation of noise is: Why
will not the private market handle the problem? No one suggests after all
that the government should regulate the production of carrots or paper clips.
What are the special characteristics of noise that could lead to some
collective policy concern?
Externalities
The most obvious problem is the simple one of externalities. When
Smith's truck rumbles down Jones' street it disturbs Jones, but Jones takes
no part in the decision as to whether or where the truck should be driven.
An externality is simply a situation where there are individuals whose wel-
fare is affected by an activity but have not voluntarily complied to take
part in that activity. The primary principle supporting the efficiency of
the outcome produced by voluntary trading among unhindered individuals is
violated. Individuals affected by some activity can not escape participation,
despite the possible detriment to their own welfare.
That noise does indeed convey externalities is made evident by the
frequently employed term noise pollution. The understanding conveyed by the
term pollution in general is that there is some commonly owned property
resource that is being exploited for individual gain. In the more familiar
case of water or air, it is that medium. When sludge is dumped in the river
it becomes less attractive for swimming. When particulate is released to the
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air, quality of breathing diminishes. When noise is generated it
is frequently said that it pollutes the airways, in the sense that other
activities (including silence) for using the airways are prescribed. A may
wish to carry on a conversation but find it impossible because the honking
of B's horn renders ordinary conversation tones inaudible. In this essay,
we shall employ the term noise disturbance where others might have referred
to noise pollution.
Externalities and Privately-Received Noise
Only a portion of the problems of noise possess the characteristics
just outlined to be associated with externalities. For example, it is fre-
quently stated that the government should have a role regulating the noise
level in factories. The argument against such participation can be made as
follows: For the most part individuals can freely choose whether or not to
work in a particular factory. If a noise situation is truly unpleasant or
detrimental to their welfare, they need not work unless an appropriate wage
differential is offered.
If all markets were functioning perfectly this argument against govern-
mental participation in the market for privately received noise would be
telling. There must be some things special about noise, no doubt
characteristics that it shares with other environmental elements, that at
least suggest the government might play a role. Two issues seem of particu-
lar interest. First, individuals may be relatively ill equipped to assess
the consequences of noise. They may understand, indeed have strong feelings
about, the level of noise disturbance. But they may not know whether or
how it will impair their hearing, mental health, or any of a variety of
other factors.
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Second, the government may have a parochial interest in noise control
to the extent that it might make transfer payments or pay for services for
those who suffer from noise. If loss of hearing raises the probability of
unemployment or a dependent welfare status, then the government may have a
strong incentive from a pure efficiency standpoint to discourage activities
that might encourage hearing loss. The same principle would apply to other
adverse consequences of noise disturbance.
This suggests that even where individuals voluntarily accept some level
of noise disturbance (what might be called contractual noise), in which case
it can be assumed that they are demanding some compensation, the government
may still have an interest in the regulation of the level of noise distur-
bance.
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2. Noise Disturbance - Special Characteristics
In what ways might the economic qualities of noise disturbance differ-
entiate it from other types of externalities, which would lead either
to different modes for assessing willingness-to-pay, or would possibly
suggest alternative procedures for improving the situation? A great number
of factors can be identified:
1) Those who suffer from noise disturbance may have considerable
latitude in reducing its effects upon them.
2) Though any particular source may affect the welfares of a large
number of individuals, unlike air pollution for example, it can frequently
be locally controlled.
3) Once again unlike air pollution or potential radiation pollution,
its dispersion and incidence can be fairly accurately predicted, for a given
location.
4) Unlike many classic examples of externalities, the effects of the
externality fall almost exclusively on individuals. The effects on firms
come only indirectly via its impact on individuals. (This situation might
be contrasted with that say of water pollution. Dirty water may make it
substantially more expensive for a variety of industrial processes that
require water to operate.)
5) The producers of the externality, and this is particularly the case
with traffic noise, are numerous, and perhaps more important, their identities
change rapidly from day to day.
6) Noise disturbance is most profitably assessed on a location specific
basis. Within a relatively small geographic area, say a few square blocks,
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the noise level may be exceedingly variable. Moreover, the valuation of
the noise disturbance may also shift rapidly from location to location.
7) In many situations, the noise disturbance shifts rapidly over the
course of the day, indeed within any hour. Individuals are likely to be
sensitive to variations in noise level, which suggests that measures that
be.
rely solely on averages willA inappropriate for individuals' valuations.
Procedures for assessing noise disturbance should recognize stochastic
variation.
Individual Latitutde in Reducing Effects
The understanding that individuals can affect the impact of noise
externalities, suggests some directions for willingness-to-pay calculations.
First, if any changes are to be made in levels of noise, a general equilibrium
framework should be employed to assess its consequences. The purpose of such
a framework would be to enable the analyst or policymaker to determine more
exactly what the change in the level of noise disturbance would be worth
to society, as indicated perhaps by willingness-to-pay. If it is mistakenly
assumed that present levels of averting activity will remain unchanged, and
if it is also incorrectly supposed that individuals will not be changing
their locations, the policymaker's determinations will be in error. Moreover,
as we shall show later in our discussion of the General Equilibrium Model, there
will be a bias toward undercrediting the gains from reductions in noise dis-
turbance and overestimating the costs of an increase in noise disturbance.
(From a policy standpoint, this will produce a bias toward the status quo.)
Second, as an equity argument, adjusting noise levels and/or providing
compensation in response to present conditions may not restore the welfares
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of individuals to the levels that would be achieved had they been given initial
property rights. If they have already undertaken substantial action to
screen out the undesirable effects of the externality, compensation for
this reduction effort should also be made.
On the other hand, if compensation is paid, or regulations imposed
employing as the model for thought the fact that individuals will not be
able to take defensive actions, either of two unfortunate consequences may
result. They may be overcompensated, or alternatively the level of regu-
lation may be set too strictly.
More than noise proofing a home or turning on air conditioning can be
done to reduce the effects of noise. Individuals can change their purchases
so that they do not encounter the noise. For contractual noise, say a dish-
washer, they can merely purchase another brand. Most non-contractual noise
bears a geographic dimension not under an individual's control. That is,
he can not buy whether or not a particular car passes down the street. In
this instance, therefore, the individual has the most significant option to
change his location. But location selection is a most particular way to
diminish the impact of externalities, and one that is insufficiently examined
in the literature. First, unlike the purchase of other goods that maintain
externalities, most individuals purchase only one location, say for their
home. Moreover, no two individuals can purchase the same location. (Although
an apartment house can replace a single family dwelling.) And
even if we look over the course of say a week to see where an individual
is spending his time in an effort to overcome single-location effects, no
individual will be able to escape the constraint that in effect he gets one
week's worth of locations. There can be no equivalent to increases or
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reductions in purchases. The strong ties of noise externalities to
suggest that some form of geographic model should be employed to assess
willingness-to-pay. Such a model is developed below under the heading
Noise and Location in a General Equilibrium Model.
Sources Subject to Local Control
The strong example in this instance is traffic noise. Whatever the
level of noise emanating from trucks, buses and automobiles, the direction
of traffic makes it possible to make one street or neighborhood noisy and
another quiet. An ideal strategy for looking at the control of the noise
externality would examine tradeoffs between controlling the level of noise
emanating from the traffic itself, reducing the amount of noise from any
particular vehicle passing any particular point, and directing the flow of
traffic, say from street A to street B. Represent these possible strategies
as X representing control of the number of vehicles in use, Y indicating
control of the level of noise emission per vehicle, and Z as representing
a strategy for influencing the location of the traffic. Any or all of
these control measures may be represented by a vector. Thus, a vector for
X might have as its elements the numbers of vehicles of different classifi-
cations identified according to the noise disturbances they produce.
Assume for present discussion that the population to be affected by
noise disturbance was either in place (so the effects of the traffic noise
upon it could be computed directly), or that the effects of any particular
pattern of noise emanation could be accurately predicted. A noise control
strategy would then consist of dealing with each one of these factors. What
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should be done with X will depend on potentialities for Y and Z and vice
versa. In general, it might be expected that if Y were readily manipulable,
then we might wish to undertake less severe efforts for dealing with X and
Z. The conceptual model implicit in such an argument has something to do
with a notion of total disturbance of the noise, which might be represented
as D = f(X,Y,Z). A priori arguments are not sufficient to make an unambiguous
determination of the structure of the f function. But intuition would
suggest that more likely than not, cross partial derivatives will be nega-
tive. This would imply, for example, that the returns to a rigid policy of
traffic control would be greatest when the vehicles themselves were creating
more rather than less noise disturbance.
If this property does hold, then different noise-disturbance control
strategies will compete with each other. We may wish to have more control
at the vehicle level, but less rigid direction of traffic patterns. A two-
dimensional cross section of the production function for noise disturbance
would have the following form.
Fig. 2.1 Levels of Noise Disturbance with Z Fixed
Number of
Vehicles in
Use
High Level of Noise
Level of Noise Emission Per Vehicle
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Effective government policy for noise control will recognize the
tradeoffs between different regulatory approaches. The mix of possibilities
may be a rich one. Policy for the control of noise disturbance is con-
fronted with an additional set of complications because noise is not an
additive commodity in the sense that total noise disturbance equals the
sum of separately calculable disturbances coming from a variety of producers.
This implies that regulatory policy for noise will have to pay particular
attention to the structure of the production function for noise disturbance.
It is to that subject that we now turn.
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3. The Production Process for Noise Disturbance
Traditional discussions treat external diseconomies as if they were a
homogeneous commodity. The total amount of the externality produced is the
sum of the amounts produced by all individuals and firms together. Let x.
identify the output of source i. Then the total amount of disturbance can
be indicated N = £x..
There are two reasons why the undesirable effects of noise should not
be thought to possess these properties. First, its incidence is a geographi-
cal phenomenon (as for that matter are many other externalities that are not
always described this way). This suggests that we should not think of a single
externality, say noise disturbance in the community, but rather something more
personalized. At the most micro level it would be noise disturbance to Jones,
noise disturbance to Smith, etc. To make the analysis more adaptable to
measurement and control, some larger unit of analysis is likely necessary.
We might then have noise along upper Main Street, noise along the downtown
sections of Elm Street, noise in the high school classrooms, etc.
Second, noise is not an additive phenomenon. This study does not
suggest what is the appropriate function for aggregating noise disturbances
emanating from different sources. But it does point out that the additive-
form simplification, despite its merits when dealing with many other forms
*
of externalities, is not appropriate for noise.
In Part I, Chapter 2 of this report, Thomas Holmes shows that the traditional
efficiency condition for externalities and public goods production holds in
the case of noise, despite the fact that noise disturbance is not an additive
commodity. At the efficient point, each producer of noise should be operating
so that his marginal cost of noise reduction just equals summed willingness-
to-pay to reduce his noise.
If there is some aggregate measure of noise that is accepted by the entire
community, then as Holmes shows, the appropriate efficiency condition is that
each noise producer must balance his cost of noise reduction against the product
summed willingness-to-pay to the marginal contribution of a unit of
reduce aggregate disturbance x his noise reduction to aggregate reduction
of disturbance.
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The problem is that the amount of disturbance, as indicated by some
willingness-to-pay notion, deriving from one noise source will be substan-
tially affected by the presence or absence of other sources. If there is a
continuous traffic background noise ranging about 50 decibels, individuals
talking loudly on the street are hardly likely to disturb someone trying to
sleep in the roadside hospital. Requiring them to whisper would not make
sense. Any measure of noise is multi-dimensional. Even if matters were
additive on each one of those dimensions, and they hardly can be assumed to
be such, that would not imply that the summary measures of three different
noise disturbances would be additive.
The whole problem of aggregating is complicated by the stochastic nature
of the noise problem. Let us assume that we accepted a single measure of
noise disturbance, say decibel level. The decibel level varies continuously
within the course of the day, indeed within each minute. Frequently statis-
tical measures are proposed as a means of dealing with this variation. Take
as an indicator the first or tenth percentile of noise level over the course
of the day. But this is just an approximation that makes the assessment
process manageable. It might be far preferable to assess the distribution of
noise levels over the day and assign some valuation function. If individuals'
valuation functions could be reduced to a few parameters, computing the mean
and the variance of the decibel level might be appropriate.
A procedure whose widespread use and tractability means that it should
at least be considered for assessing total noise disturbance would find for
each level of disturbance both its likelihood of occurrence and its valuation.
These would be multiplied together, then cumulated over all levels of dis-
turbance. The analysis might be as follows:
18
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Fig. 2.2. Density Function for Noise
Density
Community Noise Indicator
Let us denote this density function as f(N). The community noise
indicator is a variable that is expected to correlate well with the degree
of noise disturbance. Other measures might be employed. If individuals
were quite dissimilar in the qualitative aspects of noise that disturbed
them, then multiple indicators might be necessary.
This little illustration does not distinguish between noise during the
day and noise at night. If, as would seem likely, individuals feel quite
differently about noise during these periods, then it might be worthwhile
to deal with distinct distributions for the two time periods. Similarly,
it might be worthwhile to factor the noise disturbance along other dimensions.
(Other portions of this analysis discuss the importance of identifying noise
on a location-by-location basis. Indicators that take say a community-wide
view are likely to be much too aggregative.)
This analysis deals with a single indicator. It is assumed that an
individual values total noise disturbance by summing his minute-by-minute
valuations. Indicate the per minute valuation as V(N); his total valuation
of a particular distribution of noise would be:
19
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/ f(N)V(N)dN .
•'o
(For many noise indicators values close to 0 or above some quite finite
values would be exceedingly unlikely if not impossible.) The computation
of his willingness-to-pay for a reduction in noise merely compares this
integral with another one for the after-reduction noise distribution f*(N)
The willingness-to-pay would be
r r
f f(N)V(N)dN - I f*(N)V(N)dN ,
•'O ^0
which can be written
I (f(N) - f*(N))V(N)dN .
This type of valuation procedure is straightforward and manageable.
Matters could become quite complex, however, if the valuation could not
be determined by summing in this separable form. For certain individuals
it is sometimes alleged substantial changes in noise level are what is dis-
turbing, not an average level. If this were true, we might discover that
individuals would prefer to be subjected to noise distribution A or noise
distribution B rather than an alternation or mixture of the two.
What does this all suggest about the way willingness-to-pay calculations
should be assessed and employed? Quite simply, unless valuations are con-
tinuously responsive to small changes in the distribution of noise,
20
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willingness-to-pay responses may be volatile. This would imply first
that extrapolations between different points of assessment should be under-
taken with caution. Second, corner solutions should be examined, for they
may turn out to be optimal.
In the next sections we examine in detail the motivation for the
willingness-to-pay approach and some difficulties associated with employing
it.
21
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B- CONSUMER VALUATION
1- Noise as a Commodity - Difficulties In Valuation
Individuals may well have significant difficulty valuing noise as a
commodity. It is not a tangible good such as apples and pears. We rarely
purchase it even implicitly on some open market. Our reactions to noise
frequently change with exposure over time. Consumers hardly have informa-
tion with which they can sensibly determine what the long-term effects of
noise on them may be.
What should be made of this ignorance? That consumers are not informed
about the effects of noise is not sufficient grounds to argue they will
undervalue its consequences. They may exaggerate on the other side. (The
evidence suggests, for example, that individuals overvalue what physicians
can do by way of improving their health.) But it does suggest that indivi-
duals' uneducated estimates of the value of noise reduction may show substan-
tial variance about the amounts they would eventually come to if they could
be fully informed. An early issue which any policy intervention designed to
gauge consumer preferences in order to determine where regulatory policies
should be attempting to ameliorate noise levels is the issue of consumer
ignorance.
If scientific determination of the consequences of noise suggest that
individuals' assessments are systematically biased one way or the other,
the possibility is raised of a paternalistic intervention. Issues surrounding
the paternalism question are explored below.
Quite beyond consumer ignorance, the scientific establishment itself is
not fully informed on the long-run consequences of exposure to different types
of noise. How should government policy deal with uncertainties surrounding
22
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the consequences of a particular form of environmental damage? This is a
question that has been faced in other areas of environmental regulation,
though not always directly. It must be faced here.
Scientific or Governmental Uncertainty About Damage From Noise
Consider a situation where the government has determined the amounts
individuals would be willing to pay to be protected against certain levels
or types of noise. The queries have originally been raised where individuals
are not informed about the best scientific estimates of the consequences,
but must draw their own inferences. Is information of this degree of
reliability sufficient for the government to make a determination of where
noise levels should be established?
The answer, of course, is what other information might be made available.
Acton in a pioneering work on determining individuals' willingness-to-pay for
health protection conducted a survey inquiring on the value of individuals in
having mobile cardiac units available. The work provides a useful parallel.
Acton surveyed a number of individuals on this subject and recognized that
they could not intelligently assess their potential gains should these units
*
be made available. Therefore, he provided individuals with some most helpful
information. Thus, to a forty-year old male, he suggested: Your probability
of being alive because a mobile cardiac unit is available is .45%. How much
would you pay to have the unit? Clearly the answer to this question should
make more sense in guiding any policy decision on the units than the answer
to the uninformed question how much would you pay for the unit.
*
See Jan Acton, "Evaluating Public Programs to Save Lives: The Case of Heart
Attacks," RAND Corporation, R-950-RC, January 1973.
23
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Unfortunately, Acton also discovered that individuals had difficulty
interpreting the information he provided them. Thus, for example, indivi-
duals in a higher risk pool offered much less than proportionately more for
this form of protection. This was despite the fact that the dollar amounts
involved were insufficient to exert any strong income effects. It seems
that individuals think of the provision of a new service such as this one
both in its physical sense of being something provided and in terms of its
productive output.
Though this evidence is hardly conclusive, individuals who are con-
sidering policy interventions relating to noise regulation' or reduction
should expect that even "educated" answers to willingness-to-pay queries
will exhibit a variety of biases. One bias in particular, noted by Acton,
will be a tendency to anchor one's valuations. For any given individual,
or for a class of individuals with like characteristics, the value of a noise
reduction may be surprisingly insensitive to the amount that the noise level
is reduced. People may think in terms of "getting rid of noise." Given
limited familiarity with measures of noise, and/or the consequences of
exposure to it, their valuations may not be responsive to what experts might
consider to be quite extensive differentials in noise reduction. No doubt
there will be other biases in survey assessments as well. The important
point to realize is that such biases may exist.
This raises the whole issue of calibrating assessments, that is reinter-
preting them to determine what people really would pay if they understood the
*
ramifications of the choice. An alternative procedure would be to ask
*
Such "calibration" is frequently proposed for refining the information
people provide when they make probability assessments. It is well esta-
blished, for example, that untrained individuals are likely to assess such
distributions too tightly.
24
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individuals to compare their valuation of noise disturbance as determined
by tradeoffs with other valued goods bearing similar characteristics. Clean
air would seem to be a good example. What is done here is to employ another
environmental contaminant, not money, as the numeraire good.
25
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2- Willingness-to-Pay and the Determination of Noise Levels
The foundation of the willingness-to-pay approach is that we should
balance total willingness-to-pay at the margin for increased noise levels
against total willingness-to-pay at the margin to keep the levels down.
A critical problem, of course, is that since noise disturbance can not be
packaged and sold on an individual basis, as say can fertilizer or even
solid waste; there will be no market transactions to provide information
on willingness-to-pay. Indeed, as was argued in our previous section on
the Production Process for Noise Disturbance, there is not individualized
production either, at least not in the sense that the amount of disturbance
one producer generates is independent of what other producers put out.
This absence of a market where consumers and producers meet to
exchange noise disturbance creates a variety of problems. First, whatever
procedures are determined to make willingness-to-pay assessments, there can
be no guarantee that true values will be provided. Second, even if we had
exacting knowledge of willingness-to-pay, so that we would know how much
it should cost at the margin to reduce noise disturbance, we might not be
able to translate this information into a regulatory procedure. Since
noise disturbance is not an additive commodity, we can not know what each
producer could do at the margin to reduce disturbance unless we knew what
all producers are doing.
Before we discuss further the difficulties with these procedures, we
had best be clear on the motivation behind willingness-to-pay itself. Our
starting point is understanding that what we are attempting to do is repro-
duce an outcome that might resemble what the market could produce,could it
26
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function appropriately. We shall not be involved here in the intricacies
of operation of regulatory processes. That is, we are restricting ourselves
to the raw information about willingness-to-pay, not taking the logical next
step of seeing how it will be employed.
Noise and Willingness-to-Pay
The fundamental assumption of this entire analysis is that a quiet
environment, like apples and oranges and clean air, is a commodity that
individuals value. Their preferences in this regard are made evident by
their willingness to trade other valued commodities in return for a quiet
environment. That we do not observe such trading operations at work, for
the most part is an indication of the non-existence of markets in which
noise reduction can be purchased on an individual basis. Indeed, for evi-
dence that noise, or more precisely its absence,is a valued commodity we can
look to individual consumers' purchases of noise proofing materials, as well
as an array of behavior patterns that enable them to avert noisy environments.
Our later analysis will devote substantial attention to individuals' possi-
bilities for averting more disturbance and the ways that will affect
willingness-to-pay assessments.
Willingness-to-Pay - Its Theoretical Justification
Economic markets that are working in perfect fashion automatically
generate information on willingness-to-pay. It is merely the price on the
market. Every individual will continue purchasing any good until his valua-
tion of the last unit is just equal to the amount of resources that would
be required to purchase it.
27
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Public policy intervention comes under consideration when markets are
not functioning appropriately. In the environmental sphere, such interven-
tions take a variety of forms ranging from effluent charges, to prohibitions,
to approved technologies, to standards, to subsidization of certain types of
activities, and the list continues. Some of these interventions are designed
to function on an automatic basis. Others must acquire information on the
preferences of individuals and firms so effective levels can be set. For
example, if standards are to be set, we will wish to find out how much indi-
viduals value noise pollution at the margin, and how much those who produce
the noise value its continuance or increase.
Most of the interventions proposed are designed to reproduce an outcome
that to a significant extent reflects the outcome that would be achieved if
there were a functioning perfect market for the commodity. For reasons
that will be deliberated at length below, the general efficiency condition
is that for each type of noise that is received, the willingness-to-pay to
avoid a marginal unit will just equal the willingness-to-pay to produce
that unit (i.e., not be required to eliminate it).
This beautiful balance can only be achieved in traditional markets
because the transactions are actually carried out. Those who receive the
goods pay for them. Those who sell them must produce them. So long as no
individual or firm can produce the good at less than its market price, so
long as no consumer would pay more for the good than is currently being
charged for it, it is evident that no rearrangement of resources relating
to the production of that particular good can work to the benefit of all
parties concerned.
28
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In a world where efficiency is a goal, this same property should hold
true for noise. For any particular element of noise disturbance, there must
be an equilibrium in the costs to those who gain and lose from the distur-
bance. Here though the disturbance will not be individually conveyed. This
implies that we must be concerned about the total of the prices that would
be paid by all affected consumers. They are all simultaneous "purchasers."
On the production side, we must look to the producer of the disturbance who
can eliminate it at lowest cost. If the lowest cost of elimination is less
than the total amount that could be extracted from all beneficiaries, then
with appropriate side payments the disturbance could be eliminated to the
benefit of all parties involved.
This is the familiar condition for efficiency in public goods provision.
Let MRS. represent the marginal rate of substitution of individual i of some
other numeraire good for a particular type of noise disturbance. Let MC
represent the least amount of the numeraire good that must be sacrificed to
reduce the noise disturbance by one (small) unit. For simplicity, there is
no reason why money itself can not be employed as the numeraire good. The
efficiency condition is that
I MRS. 1 MC .
i
If the sum exceeded MC, then we could charge each individual his MRS, and
employ the resources secured to reduce the noise level by one unit.
29
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3- The Right to a Quiet Environment - An Alternative Approach
The framework within which a valuation question is posed can frequently
affect the answer. Once the question is raised, what is a certain reduction
in noise worth to a specific individual, we admit to our willingness to
violate what some might think of as a right. That right is the privilege
to exist in a quiet environment. Those who would maintain this right might
suggest that it should not be incremental zed away merely because the tallied
willingnesses-to-pay to preserve it did not equal the willing payments of
those who would like to generate noise.
If the issue is framed in this manner, some might argue that what is
being debated is merely the benchmark from which payments for changes should
be made. The point of initial distribution should be thought of as zero
noise, or at least some level of low noise that would be clearly acceptable.
*
But more than an appropriate benchmark might be involved. First, unless
this is a most unusual policy situation, the benchmark will be used as the
You do solve part of the nonconvexity problem if you look at what would
happen if we had a zero benchmark. All of those firms or individuals who
would reside in the now noisy area would be in to make their appreciation
of quiet felt.
This is not a bad solution as a thought experiment. In practice, it
could accomplish rather less than this, as those firms and individuals will
not be present. What could be done, of course, would be to see who is
residing in equivalent areas which happen to be quiet. The only danger with
this "ceteris paribus" approach is that we would be unlikely to find condi-
tions that are equivalent except for being quiet. For example, it is unlikely
that there is any zone along a major highway where we can show how citizens
appreciate silenced trucks and motorcars.
Without controlled experiments, it is unlikely that we will ever be
able to determine with any great degree of precision what we would like to
know: How much citizens who would be participating in the area if it were
quieted would pay to preserve (or demand to give up) their quiet sanctum.
The world just can not generate the data that we want. Any results that
were extrapolated from regression data would have to be interpreted with
great caution.
30
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point from which to measure losses, and the point at which we see who will
be involved in the market. But compensation is unlikely to be paid from the
benchmark.
Assume that a relatively low benchmark is selected; it could be a noise
that is never annoying or disturbing in any way. The use of such a bench-
mark as the starting point for policy deliberations is likely to work in
favor of those who would prefer a quiet environment. (This favoritism
could continue even if no compensation were paid for deviations from the
benchmark.) More of their quiet-preferring friends will be around to have
their preferences measured. Those who produce noise, however, would be
underrepresented at the equilibrium established from a low noise benchmark
Some of them would only bother to make their entry into the market if a
relatively high benchmark were established, will not be around to register
*
some positive wi11ingness-to-pay at the margin.
The second major problem with the benchmark approach is that it in no
way takes into account the notion of the inviolability of a right. No one
would suggest that a rapist who would pay more to rape a woman than the
woman would pay to avoid the rape should have the opportunity to do so.
Moreover, even if compensation were paid and charged, few individuals would
suggest that this activity was acceptable. Neither would we like to allow
individuals to participate in a lottery for giving up their heart, say to a
*
There is an interesting question, relating to the convexity issue, of how
much a firm or individual who would like to see a rise in the permissible
noise level will pay for increases until his entry level is reached. If
he will be charged full value once he gets to his entry level, then
he will reap no surplus later, and he should pay nothing. But if there
will be less than full extortionary charges later, then his amount may be
positive. To make this determination involves more or less a dynamic pro-
gramming approach, with the payer trying to predict whether a higher level
of noise is worth anything if it is still below the entry level.
31
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rich man in need of a transplant. There may just be a feeling with society
that some things which we may think of as rights should not be traded away.
Even to put the question into the framework of willingness-to-pay may be
degrading.
This would represent an instance where we do not wish to let unhindered
individual exchange operate. If we were forced to look for an analytic
justification for this wish, we might find it either in relation to issues
of distribution or externalities in general. Both of these are discussed in
separate sections. The distribution issue is relatively straightforward.
We do not like to see individuals subjected to what we consider unsatisfac-
tory environmental circumstances just because they are poor.
The externalities argument is merely the fact that others care when you
are subjected to noise. It may be because we are forced to share in some of
the costly consequences of that noise infringement. Alternatively, we may
just not like the idea of individuals being subjected to noise.
Although the externalities and distributional arguments may address
the reasons that we do not want individual exchange to predominate in these
circumstances, they also may not predominate. The explanation may be much
closer to the rape or life sacrificing cases. There are certain rights or
amenities that independent of analytic argument we do not like to see sacri-
ficed. If this argument is accepted, the only way the willingness-to-pay
approach could be implemented would be to ask: How much would you pay to
never be asked the question how much you would be willing to pay to accept
32
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a certain amount of noise. Convolutions such as this start to engage us in
the type of paradoxes that so excited philosophers at different periods in
the past. Perhaps it is best to merely recognize that not all parties will
accept a willingness-to-pay approach, and that the arguments against it
are not necessarily frivolous.
33
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C DEFINING THE EFFICIENT OUTCOME
!•• The Efficient Outcome Uith Noise Averting Activities
Assume for purposes of simplest illustration that all noise disturbance
was produced by a single source and inflicted its external diseconomies on
a single recipient. For purposes of discussion, let us employ the present
noise level, Nn, as a benchmark. The cost to the noise producer of reducing
noise below this level is C(N). The consumer would be willing to pay some-
thing to have the noise level reduced below NQ. Let us indicate this
amount by B(N). The lower is N, the greater will be both C(N) and B(N).
If the only variable subject to manipulation were N, and if distribu-
tional considerations were ignored, the noise level would be lowered (or
raised) to that point where the sum B(N) - C(N) is the greatest. Taking
the appropriate derivative and setting it equal to zero, the efficiency
condition is simply:
B'(N) = C'(N) ,
which can be interpreted that the marginal benefits from further noise
reduction equal the marginal costs imposed on those who must reduce their
noise.
A Model with Noise Averting Behavior
Matters are complicated just a bit if there is the possibility of noise
averting expenditures or activities. Represent these activities.as A.
These activities will be undertaken by consumers, perhaps staying away from
a traffic-noise plagued apartment during rush hours, or purchasing an air
conditioner. The consumer now reaps a gain that reflects both the noise
34
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level and the averting activities that he undertakes. Represent his ini-
tial level of averting activities as AQ, with initial noise as Nn. The
gain can be written G(A,N), a measure which arbitrarily puts G(A0,N0) = 0.
The lower is N, the greater the value of G(A,N). The relationship with A
is not monotonic however. Early averting activity for any particular noise
level may improve the situation of the consumer. But after some point,
the additional benefits of averting activity will be more than outweighed
by the costs of undertaking it. It is assumed in this analysis that income
effects are not significant; therefore G(A,N) can be defined independently
of any charges for changes in A or N.
In a world with noise averting behavior, the equivalent to the B(N)
function defined previously is G(A,N). The procedures for defining the
efficient outcome are also equivalent. What we wish to maximize is the
total net benefits to the consumer and noise producer. That is, we wish
to maximize G(A,N) - C(N). In this analysis we shall employ dollars as
the metric for which both benefits and costs are measured. This would
imply that G(A,N) can be readily interpreted as the consumer's valuation
of a particular A,N pair. We shall discuss in the section that follows the
way these valuations can be converted to willingness-to-pay calculations for
reduction in noise disturbance.
The conditions that determine the efficient combination of noise level
and averting actions are readily derived by differentiating G(A,N) - C{N)
with respect to each of A and N, and setting the derivatives equal to 0.
This yields
G^A.N) = 0
35
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and
62(A,N) = C'(N) .
The first condition is that averting activities should be neither increased
nor decreased if the object is to reduce the implicit costs of the noise
and activities to avert it. The second condition is that given a correspon-
ding optimal level of aversion activities, the noise level should be adjusted
so that willingness-to-pay for further reductions just equals marginal cost
of further reduction. (There are some second order conditions, of course.)
This result suggests both the strength and weakness of a willingness-
to-pay approach when averting activities can play a significant role. The
strength is that even in the presence of possible averting activities, the
efficient outcome when regulating an external noise disturbance is that the
marginal cost of reducing the noise equals the marginal willingness-to-pay
to avert it.
The weakness is that deducing willingness-to-pay for non-marginal noise
reduction on the assumption that averting behavior will not change will lead
to incorrect assessments. The efficiency condition that marginal willingness-
to-pay for further noise reduction just equals the marginal cost of such
reduction only holds when the level of averting behavior has been optimized
as well. The next section discusses ways to define willingness-to-pay for
noise reduction when averting behavior is explicitly allowed to vary.
Uillingness-to-Pay With Averting Behavior
Assuming that individuals would respond honestly, and accurately, what
question would we like to ask them about willingness-to-pay? The appropriate
question is the following;
36
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S(A,N)
Allowing yourself to alter your averting behavior in
response to changes in the noise level, how much would
you be willing to pay to lower the noise level N?
The relationship of this question to the above equations is now evident.
We can write A* = max G(A,N), which defines A* as a function of N. The
A
willingness-to-pay function now becomes G(A*,N), where the first variable
is understood to bear a functional relationship to the second. This whole
function might be written W(N) = G(A*,N), where W(N) represents willingness-
to-pay for achieving any particular noise level. The process can be best
understood with the aid of a graph.
Fig. 2.3. Hillingnoss-to-Pay Witn Averting Activities
N. is noise level lower than NQ
NQ is initial noise level
NM is noise level higher than NQ
A, , AQ, A., are optimal levels of
averting behavior for N, , N~,
w/fn and NM respectively
s . W(N) = Max G(A,N) = 6(A*,N)
N)
37
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The willingness-to-pay curve, W(N), is now represented by the upper
envelope curve. The efficiency condition is that
W'(N) = C'(N) ,
which is the standard notion that willingness-to-pay should be set equal to
the marginal cost of improvement. There are at least two things to note
about the W(N) function. First, except for noise levels close to NQ, it
lies everywhere above the curve for A = AQ. The way to interpret this is
that the value of noise reduction is greater if other actions can be changed
as wel1.
This result also applies when considering possible increases in noise.
Being allowed to engage in averting behavior reduces the consequence of the
loss. In sum, the curve of gain (or loss) from noise reduction (increase)
with the possibility of changes in averting actions lies on or above the curve
G(AQ,N) which assumes no alterations in averting actions are possible.
Averting Actions and Loss from Effective Noise
The second point may be a little more contrary to intuition. The slope
of W(N) over some range can be greater or less than the slope of G(Ag,N). What
is interesting is that for the same noise level, new or superior averting
capabilities may lead to less total averting behavior (measured in some units
such as dollar expenditure on averting behavior), and what is perhaps more
surprising, possibly a higher level of effective noise. Since it is more
contrary to intuition, let us illustrate the situation where improved averting
possibilities lead in fact to an efficient outcome where the effective noise
level is increased, not decreased.
38
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Fig. 2.4. Effective Noise Levels With Alternative Averting Possibilities
G(A,N)
RT--
RTT--
Situation I - Base Period
Averting
Possibilities
Situation II - Improved Averting
Possibilities
I
Dollar Expenditures on Averting Behavior
In old situation I, the optimal level of exoenditure on averting behavior
was XT. This yielded a total gain of YT. YT can be broken down into compo-
nent parts. One part is the loss from the implicit costs of averting
behavior. This has already been identified as XT. The other component is
the cost of the noise itself as indicated by willingness-to-pay. But the
noise component is modified by the level of averting behavior. What we are
worried about therefore is not the absolute level of noise disturbance,
rather the noise disturbance as perceived by the individual receiver. This
39
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received noise disturbance might be referred to as the effective level of
noise. We shall refer to the gain from the reduction in the effective
level of noise (from some initial reference level) as R. For the old
situation, it would be R,. This is merely addressing the G(A,N) function
*
in a separable and additive form. That is,
G(A,N) = H(A,N) - E(A),
where
H(A,N) = R and E(A) = X.
In new situation II, there are new and improved averting technologies.
The G (A,N) curve lies above the G (A,N) curve thus representing this gain.
Yet, in the situation illustrated, not only is expenditure on noise averting
behavior less in situation II, but the effective level of noise reduction is
also lowered. This noise reduction, from the equations above, is given as
R = G(A,N) + X .
In the diagram, it is shown that R, is greater than R,,. The initial situa-
tion had more effective noise reduction. What this implies more generally is
that no firm conclusions can be drawn about the relation between advancing
technologies for noise reduction (or noise control) and the optimal levels of
effective noise.
*
This procedure may be particularly acceptable here since N is fixed. The
only requirement is that the two contributions of A, as a cost in terms
of influenced behavior, and in terms of reducing effective noise level, be
quantifiable in the same units.
40
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This is, of course, a special situation. Generally, we would expect
that as improvements are achieved in averting mechanisms, effective noise
*
levels will be reduced. What the analysis does illustrate is that the
whole issue of assessing the damages from noise is a most complex one. Our
intuition can frequently lead us astray.
It also stresses the need to look at the measurement of noise distur-
bance from the standpoint of the individual receiver. Purely physical inter-
pretations of noise disturbance, and especially those measured at the source,
can not monitor what policymakers should be after: the amount that the
noise disturbs its human receivers.
The Implications of This Analysis
The implications of this analysis flow in two directions. First, even
assuming that those who suffer from noise could effectively coordinate them-
selves to engage in an optimal level of noise averting behavior, no firm con-
clusions about willingness-to-pay can be drawn merely by observing present
levels of suffering from noise. To make such a determination, we would have
to have information on marginal costs of noise-averting strategies that are
not being undertaken. If such strategies merely involve a foregone intensi-
fication of present strategies, monitoring marginal costs will be a pretty
routine process. But they may involve a switch in a number of actions, in
which case empirical determination of marginal costs will be extraordinarily
difficult.
Second, if EPA finds itself in a position to regulate noise and/or noise
averting behavior, it should not conclude that if there are advances that make
it less expensive to reduce or avert noise that these will automatically lead
*
The example from the text might occur as follows. Base period reduction of
20 units of disturbance at cost of $1,000. New technology permits 18 unit
reduction for $300, with further reduction very expensive and not worth it.
The improved technology leads to an efficient equilibrium where there is
less reduction in noise.
41
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to lower optimal levels of noise. Let us say that a new noise proofing
material is developed that can achieve 95% of the level of noise reduction
of present standard materials at 20% of the cost. If further noise reduction
were desired beyond that offered by the new material, it would be necessary
to revert to traditional methods. It would seem quite reasonable for
society to opt for the much cheaper new technology, and make a slight
sacrifice in terms of the level of effective noise for a substantial savings
in expenditure.
To sum up, optimal levels of noise, as determined within a willingness-
to-pay model depend both on activities available to avert the noise and the
cost of reducing the noise itself. If there are closed pedestrian malls
alongside major traffic arteries, then it may be less important to reduce
.traffic noise. If soundproofing for homes is relatively inexpensive, less
stringent standards should be imposed on noise-generating facilities in
residential areas. If inexpensive procedures are developed to reduce the
noise produced by trucks and buses, desirable levels for traffic noise are
likely to be reduced as well. If a city layout is such that individuals
can readily escape from noisy areas, then it may be less important to reduce
noise disturbances in those areas where they are significant.
Collective Action on Averting Behavior
This analysis assumed that individuals would be able to coordinate
themselves appropriately to achieve an efficient level of averting behavior
for whatever noise level happens to pertain. In general this assumption will
be valid, since most forms of averting behavior can be undertaken individually.
42
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Each individual can weigh his own costs of protecting himself against noise.
If these are the total cost, and if he is the total recipient of the bene-
fits, an efficient outcome will be achieved. Moreover, if there are many
recipients of the noise acting independently, strategic manipulation of
levels of averting behavior will not prove profitable. If say EPA charges
all noise producers the summed willingnesses-to-pay to avoid their noise
output, it would not pay any single recipient to reduce his averting
behavior thereby increasing (most likely) his willingness-to-pay and leading
ultimately to a reduction in noise level. His willingness-to-pay in itself
would change the sum for all recipients by but a tiny percent. His benefit
from the reduced noise level would be minimal, yet he would bear all of the
burden of his suboptimal level of averting behavior.
A concrete example makes the point clearly. Think of an uncoordinated
community of individuals disturbed by traffic noise. EPA is going to dis-
cover the losses imposed on the community by traffic, and then regulate
appropriately. It would surely not be in the interest of any individual to
leave his window open just to alter the EPA total, and therefore ultimately
the traffic noise.
If the community could organize itself, matters might be different.
They could agree as a general policy to leave windows open. Each would be
contributing to a collective good: a higher marginal valuation on noise
produced.
Not all forms of averting behavior will be individually purchased. For
example, placing trees at roadside along one's property may help shield noise
disturbance for all. Citizens as a whole might prefer a situation where
43
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everyone planted trees, but in the absence of coordination, no such trees
would be purchased. A perhaps more compelling example would relate to
buildings that are subjected to much public traffic. No one individually
would have much of an incentive to emplace noise insulation.
Government regulation of noise disturbance should recognize that
the structure of productive possibilities may be such that there will not
be appropriate incentives for noise recipients to engage in efficient levels
of certain averting activities. If the government can not develop other
policy measures to insure that such activities will be undertaken, it may
wish to pursue a more intensive course in the regulation of noise.
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2- Noise and Location in a General Equilibrium Model
Economists have traditionally been quick to assume that price systems
will produce stable and globally efficient outcomes in problems involving
external diseconomies. Recently the problem of nonconvexity of the recipients'
loss functions has received attention. It has been recognized that firms and
consumers may have the opportunil. shut themselves down and remove themselves
*
from the presence of the externality, and from further marginal damage.
Noise pollution involves a locational problem that vaguely suggests
the shutdown possibility, but really a quite different analytic property
applies. The situation is such that traditional general equilibrium models
do not apply, but the price system will function effectively nevertheless.
The genesis of the problem is that individuals consume not differing quanti-
ties of lots at different locations hut rather one location or another.
(We abstract from the situation where individuals purchase two or more
houses, which would complicate the analytics but not change the basic result.)
The traditional indifference curve analysis no longer pertains. The indi-
vidual's consumption choice, assuming that there are but two locations, is
between two points, not a continuum of possibilities.
But other portions of the general equilibrium model continue to apply.
Each point will have associated with it a price. The hope is that a decen-
tralized price system can be established that allows each individual to
select his most desired purchase and through that very process generates an
efficient outcome. A numerical example will make the structure clear.
See David M. Starrett and Richard Zeckhauser, "Treating External Diseconomies -
Markets or Taxes?." in Statistical and Mathematical Aspects of Pollution
Problems, John W. Pratt (ed.), Marcel Dekker, Inc., New York, 1974,
pp. 65-84, for further discussion of this issue.
45
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Optimal Assignments of Individuals
Location
M E H
I 400 (25CT) 0
Individual II ^OJT) 80 0
III 290 120
Here M is the quietest location, E second quietest and H the noisiest.
The numbers in the matrix represent the amount that each individual would
pay to have that location rather than H. For example, individual II does
not like E much more than H, but finds M much more pleasant than H. In
the particular numerical example under consideration, the three circled
numbers give the optimum assignment, with I at E, II at M, and III at H.
The total value of the allocation is 250 + 300 + 0 = 550. By comparison,
with I at M, II at E and III at H, the total value would be 480.
It is, of course, quite possible that the individuals do not even
agree on the ordering among the outcomes. Because noise is a multi-dimen-
sional commodity, this might occur even though noise by itself were the
only characteristic of importance. Some individuals may not like noise at
night, others during the day. Some may feel most strongly about peak
decibel level, others may be more concerned with the average. Some may
object to high pitched noises, others may object to traffic noise, etc.
But differences in ordering are more likely to reflect other factors such
as convenience, a very personalized commodity, or other local amenities
not related to noise.
What then of our problem, will a price system lead to an efficient
outcome? First, we should assure ourselves that there is an efficient
46
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outcome. There surely is, for this is merely the job assignment problem
*
that is well known in operations research. In that instance, the objec-
tive is to find the assignment of jobs that maximizes the total payoff to
the group, where their valuations are just added together. Here we wish
to associate individuals with locations.
It is worthwhile noting,before moving on to the question whether the
price system will support the optimal assignment,that this procedure is
perfectly general and will work if there are many individuals and many
spots available at each location. Moreover, the total spots may exceed
the number of individuals. The job assignment equivalent to this situa-
tion would have many different openings for the same position (or to keep
matters particularly pure, many replications of the same position).
Hillingness-to-Pay and Optimal Levels of Noise at Locations
If we had collected information on willingness-to-pay of individuals
with different characteristics, then in theory we would optimize noise
levels in the following manner. There are three (an arbitrary number)
different types of individuals, with willingness-to-pay for noise reduction
schedules of the form W (N), Wk(N), and W (N). (These schedules can be
a D C
calibrated from any arbitrary benchmark, for simplicity let us say a noise that
is never annoying.) The individuals are at the locations in the numbers:
Main Street Elm Street High School
Type a Mfl Eg Ha
Type b Mb Eb Hb
Type c MC EC HC
See pages 183-184 in Harvey M. Wagner, Principles of Operations Research With
Applications to Managerial Decisions, Second Edition, Prentice-Hall Inc.
Englewood Cliffs, New Jersey, 1969. This is a variant of traditional trans-
portation problems.
47
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It should be understood that these numbers need not suggest that
they spend all their time there. Some individuals could be allocated
fractionally to two or more locations. Similarly, if as expected, noise
varies over the times of day, what is called here location should be
thought of as a location-time pair.
Now it may turn out that the cost of reducing the noise on Main
Street is greater or less,depending on what is done on Elm Street. For
example, if a cheap way to reduce incidence on Main Street is to reroute
trucks to Elm Street, we would expect these cross-effects to work against
us. On the other hand, once a noise-muffling system is installed on autos
in town, there is no additional cost of quieting things down on supplemen-
tary streets. To deal with a situation where there are multiple locations,
the analysis is quite parallel, it is just that the cost function takes
the form C(NM>NE,NH); i.e., the cost of noise levels across the city must
be computed simultaneously.
The noise levels across the city must be optimized simultaneously.
Employing the same procedure as before, where the objective is to maximize
willingness-to-pay for noise levels less the cost of achieving them, the
objective function is
I- I MjWj(NM)-.EjWj(NE) + HjWj(NH)-C(NM5NE,NH) .
j-a »D,C
Three equations make up the efficiency conditions. For the noise on Elm
Street the efficiency condition is
48
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with equivalent conditions being defined for the other locations. In the
special case where the cost function can be written as a separable function
of the costs of achieving noise levels in each location, the last term in
the efficiency condition then can be written C'(Np). The interpretation is
the summed willingness-to-pay for further noise reduction at each location
equals the marginal cost of further noise reduction at the location.
Changing Locations and Willingness-to-Pay
This whole analysis has assumed that individuals will not shift their
locations after noise reduction. But that may not be the case, so there may
turn out to be more a's on Elm Street and fewer at the High School, etc.
Recognizing the possibilities for "moving around" greatly complicates the
task of computing willingness-to-pay. Merely surveying those who are pre-
sently residing in an area may not be sufficient. To take explicit account
of changes in location is the purpose of the general equilibrium analysis.
Rent as an Indicator - Sometimes Appropriate, Sometimes Not
It is sometimes alleged that a way to assess the gains from improving
environmental amenities is to determine what happens to rentals. This is
incorrect, as a simple example will make clear. Let us assume that we have
two residential areas. One is closer to town but noisier. The more dis-
tant area is sufficiently quieter that the noise factor more than balances
the convenience factor; the quieter residential section commands a rent
differential.
A measure is now undertaken to reduce the noise in the close-by area,
thereby raising its relative attractiveness. This will reduce the rent
49
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differential between the two residential sections. The total rentals
within the system will diminish. The missing factor is the consumer
surplus that the renters receive as the noise level is reduced. It
should be counted as a benefit to be added in with the gains in rentals.
(Consumer surplus will count in quite the opposite way, that is be
reduced, if the noise reduction takes place primarily in the area that is
already commanding the scarcity rental.)
There is much confusion on the rental issue, and it is important to
understand that willingness-to-pay determinations may be profitably
secured by inquiring about rents. If a noise reduction on Elm Street
were under consideration, we might inquire of the Elm Street tenants how
much additional rental they would be willing to pay at a maximum in return
for such a reduction. The answer to this question, assuming that it was
honestly and accurately provided, would tell us about the willingness-to-
pay of those presently living in the area. It would be an appropriate
guide to efficient noise-reduction decisions.
Note that this determination may differ significantly from what happens
to rentals when a noise reduction is undertaken. If present residents were
all the possible tenants in the world, and if the rental market were com-
petitive, then the rise in rent would equal the willingness-to-pay of the
individual who valued the noise reduction the least. All the remaining
tenants would reap additional consumers' surplus from the noise reduction;
that is, they would reap a gain in overall welfare since they would be
If there were other individuals in the world, one could argue they could
come in and bid up the rent. It is true that if this area is small rela-
tive to the rest of the world, and if it is the only one undergoing noise
reduction, rentals will adjust to reflect any environmental gains.
From the standpoint of EPA, however, this form of small sector of a
large system analysis will not likely be relevant. If noise standards or
other noise regulating activities are to be undertaken, it is likely that
they will be imposed in many areas. Consumers surplus gains or losses
will not be wiped out by competing w4th some grand world.
50
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charged less for the noise reduction than the amount they would have been
willing to pay for it.
This situation, idyllic for the renters, actually will not come to
pass. Rents are likely to be bid up by more than the minimum valuation
as outsiders are enticed into the now quieter neighborhood. Consumers'
surpluses for those forced out are likely to be negative. Most of those
who still reside will be reaping a positive gain, as will the neighborhood
newcomers. Two general conclusions are evident.
1} Merely asking the present residents how much they would pay to
quiet the neighborhood leaves aside the important information of how much
outsiders who might move in would pay.
2) Merely observing rental differentials between quiet and noisy
neighborhoods, or the change in rentals that occurs when a neighborhood
changes its level of noise disturbance does not reveal willingness-to-pay.
And information on that quantity, after all, is the building block of
efficiency determinations in this area.
Using Hlllingness-to-Pay When Individuals Change Locations
In the next section we present a simple numerical model which illus-
trates the way the gains to society as a whole should be computed when v/e
must value a noise reduction within a general equilibrium model. The
numerical results show in essence what is the appropriate way to value any
reduction in noise, when noise is a localized disturbance, and where indi-
viduals choose neighborhoods on the basis of the combination of rental levels
and environmental amenities. (It should be understood that rentals
implicitly applies to owner-occupied housing as well. The "rents" for such
are total monthly charges net of capital accumulation for the owner.)
51
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First, survey all individuals to see how much they would pay to live
in each possible location. The model suggests that present location
assignments have been optimized to give society the highest achievable
value in terms of summing up the residents' valuations for where they live.
This allocation is readily determined, as we shall show later, by letting
the price system function in a manner that permits rents to,.reach
competitive levels.
Second, survey all individuals to see what would happen to their
valuations in response to possible changes in the level of noise distur-
bance at one or another location. Then determine the manner in which indi-
viduals will shuffle their locations in response to the reduced noise
disturbance and changed valuations. Or to say the same thing in different
words, determine the new highest achievable value for the society as a
whole. The summed willingness-to-pay for the noise reduction at that loca-
tion will equal the difference between the present highest achievable value,
and the one for the world before the noise reduction.
If the cost of the noise reduction is any amount less than this cru-
cial difference, then it would be inefficient to forego the reduction.
(Efficiency here is understood in terms of Pareto optimality. For a situa-
tion to be inefficient, there would have to be an achievable distribution of
charges for the costs of reducing a noise disturbance such that assessing
the charges and carrying out the reduction made some individuals better off
and no individuals worse off.) If the cost of the noise reduction were
greater than the crucial difference, then undertaking the reduction can not
be to the benefit of all parties concerned; it can not represent a move to
a Pareto superior position.
52
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The analysis below just looks at a noise reduction of a particular
magnitude. la a policy context, there may -^eU bfc some "\atHutte to deter-
mine the extent of the reduction in disturbance. The ability to make
adjustments in the magnitude of the reduction in no way complicates the
apparatus for calculating efficient outcwres. Vie w>vrtti oust have to com-
pute the gains in total value for in between levels of reduction. Reduc-
tions would be continued until the marginal cost of further reduction
just equalled the marginal ga^ ™ the tota"\ vacation to society for the
optimal allocation of locations. The exact procedures can perhaps be
better understood with the aid of a numerical example.
A Simple General Equilibrium Example
Our simple general equilibrium model involves three locations, each
with a capacity for three tenants, and nine individuals. Location A is
generally considered to be the most attractive location, a factor which
reflects matters such as convenience and cleanliness as well as the noise
level. B is the second most attractive; on average it receives lower
valuations by individuals. C is the least attractive.
To secure the valuations of the individuals for the three different
locations, we employed a computer-based random number generator. The values
for location A were chosen from the uniform distribution with endpoints at
100 and 200; those for B over the interval from 50 to 150; and those for C
from the interval 0 to 100.
53
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Locations
Individuals
6 105.07 108.27
7 149.43 110.76
8 121.32 100.75
The optimal location algorithm assigns three of the nine individuals
to each of the three locales. As shown by the circles, it places indivi-
duals 3, 4 and 9 at A; 1, 2 and 6 at B; 5, 7 and 8 at C. The total score
over all the locations is 995.02.
The Optimal Assignment Algorithm
Before turning to the critical policy question, what will a noise
reduction be worth, it is worthwhile to observe the way the optimal assign-
ment procedure is conducted. It turns out to follow a straightforward market
simulation. This implies that real world markets could (and to the extent
that there are not imperfections in them do) operate in the same manner.
Initial prices, the p^OVs, are set for the three locations. Good
starting points are expected values (150, 100, 50 in this example) or actual
averages of valuations drawn from the sample. Individuals are then "told"
54
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to identify their highest value location net of price. Individual 3,
for example, gets net values of 6.13, 17.07, and -2.78. Then each indi-
vidual is assumed to demand his highest value location. This is the
location where he would get the highest net payoff if he had to pay the
"rental price." Individual 3 demands location B. Excess demands, the
D. 's, for the locations are computed by adding up the number of individuals
who want each and subtracting out the spaces available. It is then time
to determine a next round of prices to diminish these excess demands.
The algorithm employed was
where i indexes the locale and 6 is some arbitrary small value. The pro-
gram converges swiftly to the optimal allocation.
Valuing a Reduction in Noise Disturbance
Now that we understand how individuals are optimally allocated (or
given the pricing algorithm allocate themselves) to locations, we can
compute how much a noise reduction is worth. To illustrate, let us
inquire what it is to have a noise reduction of say ten points in the
community noise index at location A. There are no changes in noise distur
bance elsewhere. To give a simulated answer, we added a random number to
individuals' original values for location A. The random numbers added
were chosen from the uniform distribution over the interval 0 to 100.
(Individual 9 had 30.72 added to his score, by way of example.)
55
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If the location assignments had stayed as they were, that is if
there were no possibility for rearrangement, the total score would
increase to 1063.98. (Individuals 3, 4 and 9 gained 68.96 between them.)
This implies that if a willingness-to-pay survey were taken of the indi-
viduals in the location that would receive the noise reduction, the total
assessed gain would be 68.96.
Locations
ABC
1 218.6047250000 (l46.330601OOOj^ 36.5172801000
2 139.6452770000 84.1127996000 (35.524360200^
3 159.2590500000 ^17.066500000?) 47.2205200000
4 (164.837002000?) 53.3606901000 2.6460849900
Individuals 5 172.1546650000 89.9669600000 (^9.1291599000"
6 162.2032720000 Q08.2716000000) 53.9786301000
7 (|l7.4936430QOo3 110.7551000000 69.6862202000
8 169.5423200000 100.7546000000 (62.6318402000"
9 (JJ?9.723629000(T) 50.3099799000 30.8650200000
Real location possibilities increase this gain. Individuals 2, 3 and
7 shift locations. The total score increases to 1121.01. The social
return from this particular reduction in noise is 125.99 = 1121.01 - 995.02.
It is worthwhile to note that an extrapolation of standard pricing
algorithms will support these equilibria. That is, if every individual
looked at the prices charged for the different locations and went to the
location offering the highest return net of price, a socially efficient
56
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allocation would be achieved. Moreover, equilibrium prices can be deter-
mined by programs that produce marginal price adjustments in response to
excess demands. The prices for the three locations before the noise level
were 87, 48 and 0. After the noise reduction, the prices changed to 147,
53 and 0. (The expected values for the prices before the random numbers
were drawn were 100, 50 and 0 before reduction, and 150, 50 and 0 after
reduction.)
Implications of the General Equilibrium Model
What lesson should be drawn from all of this? First, if rental prices
adjust in a traditional manner to changes in environmental amenities, effi-
cient equilibria will be achieved despite the discrete nature of the oppor-
tunity sets for individuals. Second, willingness-to-pay surveys that
attempt to assess the value of reductions in noise levels should look not
just to the individuals resident in the area, but future potential residents
as well. Surveying merely the first group will always give a lower bound on
the value gained should noise be reduced. (This argument is made independent
of any distributional considerations.) Alternatively, if a relaxation in
noise level is being considered, surveying only those who are in the geo-
graphic area that will suffer will provide an upper bound on the amount of
loss. These two results together offer a general principle. If willingness-
to-pay assessments are addressed without regard to possible changes in loca-
tion, the policy conclusion will always be a bias toward the status quo.
There is a further implication of the general equilibrium model that is
almost a byproduct of its overall structure. The control of noise disturbances
57
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should be a localized phenomenon. It will not in general be optimal to
have the same level of noise disturbance in all locations. Neither will
it be optimal to have all producers of like noise, say all truckers or
operators of factories, to reduce their noise disturbance to the same level.
The level that will be optimal in each instance will depend on the numbers
of people who will be subjected to the noise, the way they will feel about
it, and what other individuals become involved with the noise should its
level be changed.
Just knowing that noise levels should be responsive to local condi-
tions gives us no final information as to how responsibility for noise
control should be shared among different levels of government. But it
does tell us that we should be hesitant before extrapolating results derived
from willingness-to-pay surveys conducted in Boston to all other metropolitan
areas, or indeed to other sections of Boston.
58
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3- Putting Willingness-to-Pay to Work in a Dynamic Context*
Traditional willingness-to-pay approaches start at the present situa-
tion. This presents a variety of difficulties:
1) This is an acceptable procedure for looking at local changes, but
not those that are global. If substantial changes were being considered,
then there might be some parties who would benefit or be hurt, yet who are
not represented in the present situation.
2) There may be inertial costs associated with the present situation.
Individuals or firms may have already accommodated to extant rules and regu-
lations. This raises problems of both equity and efficiency.
3) The present situation is likely out of equilibrium. Therefore all
of the values that are observed or prices in the market may not be good indi- £ J
f * 'V
cators. This would imply that we could only extrapolate to a limited J's
extent. CQ
4) Individuals or firms may have already made defensive expenditures, ",
thinking matters will not change significantly. This may raise questions of *'*»•
compensating for past inequities, or of continuing present situations even if |
they are not fair. *4»
ft
The difficulty is made particularly evident if we look at two situations, vilj
one where defensive expenditures have already been made, so costs of con-
tinued high noise levels are rather minimal. Yet in a parallel situation
where individuals may not have yet soundproofed their house or purchased air
conditioning, let us say, then it will be seen as more pressing to reduce
sound levels. The analysis that follows shows how costs of moving from the
present situation should be taken into account in the efficient regulation
of noise disturbance.
*
Neil Goldman provided valuable assistance with the mathematics and calcu-
lations in this section.
59
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Most traditional analyses invoking willingness-to-pay considerations
are employed to determine a static optimum. A few look to optimal long-
run dynamic relationships, in which case costs and benefits of alternative
strategies are cumulated via some discounting procedure. Recognizing that
the limitations imposed by starting conditions may be significant, real
world policy prescriptions should rely on dynamic assessments.
Residential locations, traffic flows, noisy equipment and noise averting
behaviors are all in place and have been optimized given current regulations
and present noise patterns. Moreover, willingness-to-pay determinations as
assessed through contemporary surveys all reflect the present situation. If
we could start over, all of these parameters might take on substantially
different values. But if there are significant costs to changing the para-
meter values from those that presently exist, that fact should be recognized
in any long-run analysis.
If buildings are already soundproofed, it is less desirable to reduce
the noise from traffic flowing around them. If traffic patterns, hence
commercial and industrial locations, are already established, it will be
more costly to change traffic flows to reduce the incidence of noise on
human beings. If noisy washing and drying machines are in place, it will
be more costly to reduce effective noise levels from such appliances. These
are all categories of problems with which we are likely to be thoroughly
familiar. Costs of transition to superior equilibria must be recognized.
To illustrate, using our previous notation, let us assume that initial
averting and noise levels are AQ and NQ, where AQ has b«?en selected to
60
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maximize G(A,N), given N». The per period gain of continuing at this
level is G(A0,NQ), which has arbitrarily been defined to be 0.
Now we recognize that because of the existence of uncorrected market
failures in the past, these levels may not be appropriate. What new levels
should be invoked? Represent the transition costs to a new level of
averting activity as S(A|AQ) and the transition to a new level of noise as
T(N|NQ). (Assume that the cost of getting to a new level is independent of
the speed with which it is achieved, which would imply the transition would
be immediate.) The object then is to find optimal levels A** and N**.
(The double asterisk distinguishes these optimal levels, where transition
costs are included, from the optimal levels determined with zero transition
costs, for which a single asterisk is used.) The costs associated with
noise and its control include both transition costs as well as the period
costs of averting behavior and noise reducing behavior. Employing a period
discount rate of r, what we wish to maximize is:
t=0
(G(A,N) -
- S(A|AQ) - T(N|NQ)
A Numerical Example
How do these optimizing conditions work out in practice? The best
way to give a good intuitive feeling for the answer is to work out a
simple example. The properties of the G(A,N) function are perhaps most
simply understood if we break it into two parts. The first, H(A,M),
reflects the consumers' actual feelings about the averting actions-noise
level pair. Thus H(A,N) can be interpreted as a willingness-to-pay
figure for an effective level of noise. The second part, E(A), relates how
much it costs to undertake averting behavior. For the purposes of this
example, then we write
61
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6(A,N) = H(A,N) - E(A) .
Define a function H(A,N) to represent the per period gain or benefit
(it could be negative) from being at a level of averting activity A and at
a noise level N, as opposed to some arbitrary reference levels. The period
costs of averting behavior and noise reducing behavior are defined as E(A)
and C(N), respectively. Ignoring transition costs to new levels of A and N,
optimal levels A* and N* are determined by maximizing period returns to
noise averting behavior and noise reduction. Employing a period discount
rate of r, the function to be maximized with respect to A and N is:
(1) I -L~. r[H(A,H) - E(A) - C(N)] .
t=0 (Hr)t
Transition costs are now introduced and their effect on the optimal
values of A and N is determined. The initial noise level NQ is taken to be
a non-optimal level (greater than N*) without transition costs, and AO is
the optimal value of A corresponding to this fixed value of N, determined
from equation (1) with N = Nn< We then represent the transition costs to a
new level of averting activity as S(A|A~) and the transition costs to a new
level of noise as T(N|NQ). It is assumed that the cost of getting to a new
level is independent of the speed with which it is achieved. This implies
that the transitions are immediate and involve "one time only" costs. New
optimal levels A** and N**, are determined by maximizing
(2) I -— T[H(A,N) - E(A) - C(N)] - S(A|A) - T(N|lU = F(A,N)
For ease of analysis, the scaling for the variables A and N in the
function H(A,N) should have the properties that: As A increases with N con-
stant, 8H/3A decreases, and as N increases with A constant, the absolute value
62
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of 3H/3N increases, and that of 3H/8A increases. In other words, as the
level of noise averting behavior increases with noise "level constant, the
marginal gain, or decrease in damage, decreases and as the noise level
increases, with a constant level of averting behavior, the marginal damage
from noise increases. Also as the noise level increases, the marginal gain
from an increase in averting behavior increases. Moreover, neither E'(A)
nor C'(N) should be decreasing. If the world is well behaved, it should be
possible to scale A and N so that all these conditions are met. (One
possibility would be to measure both A and FJ on a dollar cost basis.) We
shall employ the above-mentioned properties in structuring our numerical
example, where both the level of averting behavior and the noise level might
be thought of as involving physical units.
Note that we should expect A** and N** to satisfy
A* < A** < Aj and N* < N** < NQ .
Clearly, the smaller the transition costs, the closer the new optimal levels
will be to A* and N*.
A Numerical Example
The entire procedure might be more easily understood with the aid of
particular functional forms and a numerical example. Let
H(A,N) = K - D(N-A)2
E(A) = A2
C(N) = (30-N)2
where K and D are constants. Note that we must have A,N >_ 0. (For this
functional form to make sense, A <_ N.)
63
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a) Zero Transition Costs
The optimal levels of A and N, assuming no transition costs and both
A and N subject to control, are obtained by maximizing equation (1). Those
levels are given by:
= 30(D+1) = 30 _ A*
^ '
-
2D+1 ' 2D+1
Fixing N at a value NO, where it would be presumed in the absence of
* D
regulation that NQ > N*, results in an optimal A given by AQ = -^- NQ.
b) Transition Costs
Assume that transition costs can be written in the following way:
S(A|A*} = SQ(A-A*)2 and T(N|NQ) = TQ(N0-N)2
where SQ and TQ are constants.
The optimal levels of A and N, derived by maximizing equation (2),
can be written as:
[R(D+1)+T0]S0A* + RD(30R+TQN0)
**
A
[R(D+1)+S0][R(D+1)+T0] - (RD)2
(3)
* i- ER(D+1)+S0](30R+T0N0)
**
[R(D+1)+S0][R(D+1)+TQ] - (RD)2
1+r
where R = - . In the table below a discount rate of 10% is used.
64
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Zero Transition Costs Transition Costs
Case 1
D = 7 A* = 14.0 N* = 16.0 SQ = 5.0 TQ = 3.0
A* = 17.5 NQ = 20.0
A** = 14.99 N** = 16.97
Case 2
D = 7 A* = 14.0 N* = 16.0 SQ = 5.0 TQ = 3.0
Higher starting * _ „, RR ., _ „,. n
noise level A0 " 21'88 N0 " 25'°
than Case 1.
= lg 23
Case 3
D = 2 A* = 12.0 N* = 18.0 SQ = 5.0 TQ = 3.0
A^ = 16.67 NQ = 25.0
A** = 13.47 H** = 19.43
Case 4
D = 2 A* = 12.0 N* = 18.0 SQ = 10.0 TQ = 5.0
Case 3. A** = u>21 N^ = 20>2Q
The traditional theory of externalities suggests that if producers
are charged the marginal costs they impose on the rest of society, an opti-
mal level of externality-generating activity will be determined. We shall
now show that this result continues to obtain in the case where there are
transition costs away from the initial equilibrium.
First, we must know how much noise costs society at the optimum. It
can be seen that the positive or absolute marginal cost of noise to consumers
65
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evaluated at the optimal levels of A and N, given by equations (3),
can be represented by
X** = X(A**,N**) = - f|J(A**,N**) .
Assume that this cost is charged to the producers of noise as a per unit
effluent charge.
Let us now look to identify all of the costs of noise that will be
borne by the producers. These are the costs they will consider in deter-
mining their output decisions. The costs fall into three categories: the
effluent charges, the per period costs of the noise level, and the transi-
tion costs. The expression in equation (4) shows these respectively as
the terms X**N, C(N), and T(N|NQ). The first two terms must be cumulated
over all future time periods. We represent the discounted sum of the noise
producers' costs as P(N), where
(4) P(N) =
t=0
(Hr)
[X**N + C(N)] + T(N|NQ)
Evaluating 3F/3N in equation (2) at the optimal levels, A** and N**,
yields an expression identical to -P'(N**). By definition of the social
optimization of F(A,N), |j^(A**,N**) = 0, implying that P'(N**} = 0.
(.Assume that P(N) has only one extremum in the relavant range of N, which
it will for well behaved functions of the type we have specified.) We have
shown that from the producers' standpoint, the optimal level of noise asso-
ciated with minimizing P(N) is N = N**. What is significant from a policy
standpoint is that this is the same optimal level that was defined in our
grand social optimization. An effluent-charge-type scheme works even with
transition costs.
66
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An illustration of this result is given by substituting the functions
of our numerical example into equation (4)., and optimizing. The resulting
optimal level of N is given by:
(5) N = pjKOOR + TQN0) - RD(N** - A**)] .
From equations (3):
(R+Sn)(30R+TnNn) - (R+Tn)SJ\*
(5) N** _ A** = u _ y_y _ u J u
[R(D+1)+S0][R(D+1)+T0] - (RD)2
Substitution of equation (6) into equation (5) yields N = N**.
It is worthwhile to inquire what happens if we set the charge for noise
at too high or too low a level at the outset? The answer is nothing at all
so long as we continue to reduce the noise level until the computed marginal
social cost of noise just equals the incremental cost of proceeding further.
So long as we do not stop along the way in such a process, in which case
transition costs might mount, this will lead to the N** optimum. Say we
start with an effluent charge that is too low. Producers will have the
intention to engage in a level of noise reduction that is insufficient. The
marginal social cost of noise for their intended level will be above the
original effluent charge. The effluent charge will adjust upwards, and the
producers will develop more significant levels of intended noise reductions.
Through such a process of adjustment of effluent charges, intended noise
reductions, and computed marginal social costs of noise, an equilibrium will
be reached where the effluent charge just equals the marginal social cost
of noise. This occurs when N = N**.
67
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D. IMPLICATIONS AND CONCLUSIONS
1. Alternative Methods of Assessing Hillingness-to-Pay
This analysis has concentrated on identifying the appropriate questions
to ask when we wish to determine optimal levels of noise reduction, or
optimal regulation standards and procedures for noise. Once we know the
right questions to ask, we must develop ways to ask them.
There are three basic approaches to the problem of assessing willingness-
to-pay for reduced noise levels. The first involves merely asking indivi-
duals how much they would be willing to pay for certain levels of noise
reductions. The second looks to market transactions to see how much indi-
viduals have been implicitly willing to pay in other contexts for noise
reduction. The third approach attempts to determine what individuals should
be willing to pay for noise reduction. It starts by assessing the harm
that the noise produces. It then looks to the costs of remedying part or
all of the harm and the implicit costs of various levels of noise-averting
activity. Through an examination of the harm that is done, and the costs
of correcting or avoiding it, an assessment is made of just how much the
noise costs the recipients.
These three procedures have competing advantages. Some will be more
appropriately employed in one context; others in others. Since the whole
process of determining willingness-to-pay is such a difficult and imprecise
matter, it will frequently be worthwhile to conduct such assessments in two
or three different forms. Hopefully, there will be a fair degree of agree-
ment among the assessments. If not, we will have at least learned that one
or more assessment procedures is subject to significant biases.
68
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Inquiring of individuals directly has the advantage of securing pre-
cisely the information that is desired. One can ask any relevant group of
individuals, not merely those who happen to be purchasing particular sets
of goods. It also allows analysts to pose speculative questions about noise
patterns not presently the subject of individuals' experiences.
The disadvantage of this direct approach is that individuals may not
give accurate answers about what they really would turn out to be willing
to pay. First, they may have substantial difficulty understanding what
alternative noise levels represent. They will be expected to cast them-
selves in the unfamiliar situation of purchasing something that is not
normally for sale and which they have never purchased directly. Some of
the consequences of their purchase, for example hearing loss or mental dis-
turbance, may be poorly understood by them, and indeed as well by those who
pose the questions. Finally, even to the extent that noise recipients
understand the questions, they may have the incentive or feel they have the
incentive to distort their answers. If they believe the number they provide
will be used in policy determination, they could bias their answers to
influence the ultimate policy choice. For example, those who are the likely
sufferers from a noise externality will give high willingness-to-pay figures
if they assume that they will not be charged for noise reductions that might
be undertaken in response to those high figures.
There may be other reasons for providing biased answers. One further
example suggests the range of possibilities. It is frequently alleged that
persons interviewed tend to bias their answers toward what the interviewer
69
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expects. Anyone conducting a questionnaire on noise will clearly be
interested in that subject. The individual interviewed may give a nice
high assessment to show that he too is concerned with the area. Indeed,
*
the very fact of the interview may stimulate his concern in the subject.
The market-observation procedures would be most attractive if the
commodities whose values we wish to assess could be found in the market.
Of course they can not. Noise is not bought and sold. Where it is
implicitly priced, as say with rental housing, it usually comes along with
lots of additional attributes. For example, traffic noise is likely to be
accompanied by vehicle-produced air pollution. This would imply that any
assessment procedure would have to disentangle these accompaniments.
In this analysis we have suggested that rental differentials may be
highly misleading indicators of the value of the differentials in noise
disturbance. Unless individuals are identical in their valuation of noise,
the rental differentials between high noise disturbance and low noise dis-
turbance locations will not necessarily reflect the valuation of the average
**
individual in either location. The rent differential certainly does not
Consider the following thought experiment. Ask ten different standardized
groups of individuals how much they would pay to achieve a reduction in a
specific one among ten different types of environmental degradation. Then
scale the sizes of reductions so that the amounts paid were the same for
each, i.e., a 10% reduction in air pollution, 35% in noise disturbance, etc.
Now ask an eleventh group with the same standardized composition as the other
ten how much it would be willing to pay to get one of the ten reductions
identified. The particular reduction it will receive will depend upon a
random device. The hypothesis that once a concern is singled out it becomes
more highly valued would suggest that the answer from this eleventh group
will be below that for the ten identified levels of specific types of degra-
dation.
**
If these were the only two locations, and if they were identical on all other
characteristics, then the rent differential would reflect the valuation of
the likely few individuals who were indifferent between the two places. It
is quite possible that all of those in the noisy locale would pay far less
than the rent differential to get it quiet, whereas those in the quiet loca-
tion would pay substantially more than the differential to keep it quiet.
70
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tell us how much it would be worth to make it quieter in the noisy location,
indeed since those individuals are not seeking to move, it would represent
an overassessment.
One major problem then with market based assessments is that they can
not take into account the to be expected difference in the preferences among
the human beings who choose to reside in different locations. A second
problem is that the noisy and quiet neighborhoods are highly unlikely to
be equivalent on a great number of other variables. With a statistical
analysis, say a multiple regression, one can hope to correct for these other
factors. Realistically, analyses based on such procedures are unlikely to
provide the type of unequivocal information on which we might like to base
policy. There is likely to be a multitude of variables to correct for,
and only a relatively limited sample size.
The third procedure, where we implicitly attempt to determine what
individuals should be willing to pay for noise reduction, is perhaps the
most difficult to put into practice. There are two major problems. First,
we do not really know what the long-term consequences of noise exposure
will turn out to be. Second, the disadvantageous impacts of noise are only
partly in the monitorable effects. The what is it worth approach runs into
great difficulty when it must confront questions such as: In addition to
hearing loss and other possible consequences, what is it worth just to avoid
the disturbance? In order to address this question, it would seem, we would
be driven back to the willingness-to-pay survey approach with which we started.
This third procedure, it is worth mentioning, has frequently been
employed when we have attempted to value alternative health interventions.
The usual inputs are days of morbidity and probabilities of mortality, which
71
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are then weighted by foregone earnings on those days or years. In most
instances this estimation procedure would seem to give a lower bound; it
leaves out the way people feel about being healthy. The point is made
especially strongly when we observed that it implicitly values the morbidity
of retired individuals at zero.
What then should be done? This analysis suggests that any approach
should be thought of as an uncertain venture. An estimate derived through
any one procedure would be open to some of the methodological objectives
raised above. A mixed strategy might seem called for. Each of the three
procedures should be invoked, and through what might be called a triangula-
tion procedure, it might be determined whether they point toward common values.
It would seem essential then that an effort be made to conduct at least
two of three very different types of procedures for assessing willingness-
to-pay. If it is thought initially that one of the three approaches is most
valuable, then perhaps the bulk of resources should be directed toward it.
But it is unlikely that a 100% allocation of funds to a survey approach will
prove nearly as informative as 80% to survey, 10% to market assessment,
10% to "how should it be valued." Even if the lesson of the pilot study is
that from that point forward all analyses should be conducted by survey,
the information that the survey approach was in line with the other two
means of generating values would likely prove most reassuring.
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2. Conclusion
This analysis highlighted the characteristics of noise disturbance
that make it like and unlike other economic goods. A variety of factors
were identified that might justify some form of government intervention
into the largely nonfunctioning market for noise disturbance. If the
government is to intervene on a sensible basis it will have to know how
much it is worth to achieve a reduction in noise disturbance. Since the
beneficiaries of such a reduction are almost exclusively individuals as
opposed to firms, the government must start its policy formulations by
determining individuals' willingness-to-pay for a less disturbing level
of noise.
The willingness-to-pay determination for noise is much more compli-
cated than it is for most goods, including a variety of other external
diseconomies. First, the analyst must take into account the opportunities
for noise-averting behavior. Second, he must allow for shifts in equili-
brium residential and work patterns in response to changes in noise distur-
bances at a variety of locations. Third, he must allow for the transition
costs to whatever new equilibria will be produced by government interven-
tion. Despite the many complications in the approach, willingness-to-pay
is still the key input the government should search for when attempting
whether and by what amount to reduce noise disturbance.
Individuals may have grave difficulty providing information of their
willingness-to-pay for noise reductions. They are unlikely to be able to
predict the consequences of long-term exposure to noise with any precision.
73
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Moreover, they may have a variety of incentives to distort their answers.
Assessment procedures that attempt to determine willingness-to-pay by a
look to rental differentials between quiet and noisy locations will run
into different sets of methodological difficulties. So too, attempts to
price out the consequences of noise disturbance are likely to lead to biased
and imprecise assessments.
An intelligent assessment of willingness-to-pay will start with an
understanding of the array of complicating issues discussed in this paper.
It will employ whatever information it can secure by each of a variety of
approaches in an attempt to arrive at some reasonable estimates.
Too frequently a policy issue is neglected because the measurement
problems make it most difficult to determine with precision just the appro-
priate level of activity. This may well have been the case with a variety
of types of noise disturbance. At this juncture it would surely seem
worthwhile to take a preliminary step and attempt to make a determination,
however crude, of just what a quieter environment is worth. With that
knowledge as the starting point, we can proceed to a more effective policy
for controlling disturbance from noise.
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CHAPTER III
1
THE PRICING OF AGGREGATE NOISE DISTURBANCE
by Thomas Holmes
Introduction
The object of this chapter is to determine efficiency criteria for
the abatement of aggregate noise disturbance. Aggregate noise
disturbance is a physical property of a geographic location and is
to be distinguished from the noise emission of a particular one of
many local noise emitters. A typical and important instance is the
aggregate noise disturbance produced by a congestion of trucks,
busses, automobiles and motorcycles in a busy urban area. This
example is chosen because traffic noise is one of the most common forms
2
of noise disturbance and because it illustrates most of the econ-
omically relevant properties of the aggregate noise disturbance
phenomenon.
Aggregate noise disturbance is readily indentified as a form of
pollution to which much of the theory developed for other forms of
pollution applies. However, each form of pollution has distinguishing
properties that must be accomodated by the general theory. At least
1. I am indebted to Richard Zeckhauser and Harold Payson III for
clarification of many points in my interpretation of the mathe-
matical development reported in this chapter, although I bear
responsibility for accuracy of the results.
2. U.S. Environmental Protection Agency, The Economic Impact of
Noise (G.P.O., Washington, D.C. 1971) p. 47.
75
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three distinguishing properties of the aggregate noise disturbance
phenomenon are described in Sections A and B of this chapter. This
discussion of the properties of noise, along with a discussion of public
goods theory in Sections C and D serve to motivate a theorem on the
pricing of aggregate noise disturbance in Section E. The theorem and
its corollary are proved in Section F. Section G is given over to an
interpretation of the theorem.
It will be shown that the price theorem is consistent with the general
efficiency criterion: the efficient level of aggregate noise abatement is
such that the marginal benefit of its provision is just equal to the mar-
ginal cost of its production. The price theorem implies that to achieve
this condition each noise producer should equate his cost of noise abate-
ment to the product
summed individual
willingness-to-pay prices
for aggregate noise
abatement
marginal product
of producer's own
noise abatement in
the production of aggre-
gate noise abatement.
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A. Location Specific and Periodic Properties of Noise.
Any measure of aggregate noise disturbance denotes the disturbance
3
at a specific geographic location. In principle, the boundaries of the
relevant location can be as narrow as an individual's personal property
or as broad as a city or larger administrative unit. It seems practical
to choose boundaries such that the level of aggregate noise disturbance,
as measured by some generally accepted procedure, is uniform within
them. In this chapter, we assume that the relevant locations have been
determined by a "Noise Control Board" (NCB) having legal jurisdiction
over these locations. For example, we may be concerned with noise
' *
disturbance in the vicinity of a central highway passing through town. |' \,-
i.-; '•/
It would not be unreasonable to suppose that all of the aggregate noise J; *
!' ?
<• ',-:
disturbance in this area is caused by passing traffic. Henceforth, " '
' ' l
reference to aggregate noise disturbance always means aggregate noise ; ^
I ••
disturbance at a specific location, if the location is not otherwise '" '
mentioned. ' );:
t . '
< -(•
The relationship between time and aggregate noise disturbance dis- • !,,f
tinguishes noise from some other common forms of pollution. Noise
disturbance, like other pollutants, varies continuously with time. This
relationship can be thought of as a non-negative function. In the very long
run, a non-negative,continuous function either increases without bound or it
3. The implications of noise disturbance as a location specific phenomenon
are developed in'Chapter 2 of this report.
77
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has an upper bound; if it is bounded, then, among various possibilities,
either it converges to its bound and becomes a constant function, it
exhibits some or all of the features of a periodic function, or it is
random. Many forms of pollution are not periodic; for example, parti-
culate pollutants probably increase more or less monotonically and
either converge to an upper bound or are explosive. Noise disturbance,
however, is both bounded and periodic with a period of one day, at
4
least in the case of traffic noise.
First, the upper bound; the physics of sound teaches us that in
the audible frequency range (16 to 20,000 cps),sound levels in ex-
cess of 120-130 decibels cross the threshold of pain; at levels in
excess of 165 decibels damage to the ear is likely to occur and the
phenomenon cannot properly be described as sound. The periodic
variation of noise over time is merely the result of sleeping and
waking habits. As the volume of traffic picks up in the early
morning hours, so does the level of noise disturbance; the level
of noise disturbance remains high during the day and evening, with
peaks during rush hours, and declines after midnight as the volume of
traffic subsides. Variation between the aggregate noise disturbance
4. Long-term.cummulative effects on human health are implied by
evidence that long-term exposure to high noise levels causes
permanent hearing loss. See U.S. Environmental Protection Agency,
Public Health and Welfare Criteria for Noise (GPO, Washington, D.C.,
July 27, 1973) p. 5-27.
5. Lyle Yerges, Sound, Noise and Vibration control (Van Nostrand
Reinhold Company, 1969) pp. 10-11; U.S. Environmental Protection
Agency, Public Health and Welfare Criteria for Noise (GFO, Wash-
ington, D.C., July 27, 1973) p. 5-12.
6. For systematic description of typical noise disturbance patterns,
see U.S. Environmental Protection Agency, Community Noise (GPO,
Washington, B.C., 1971).
78
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of day and night tends to be regular. Thus, the aggregate noise disturbance
phenomenon can be completely characterized for the medium-term future
by a description of the level of aggregate noise disturbance as a function
of time over a typical 24-hour period. Long-term adjustments to the amplitude
of the function can be made to represent long-term changes in the factors
producing aggregate noise disturbance.
The two properties of location specificity and periodicity greatly
simplify the measurement problem. Data on aggregate noise disturbance
is required for a given location only for a typical 24-hour period.
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B. The Many Sources of Noise and Stochastic Measures.
A third property of aggregate noise disturbance is that
it emanates from a large number of different sources, as the
example of traffic noise illustrates. In other studies, this
situation is referred to as one of many polluters contributing
to the same type of pollution, but, to my knowlege, this common
phenomenon has not been given the systematic analysis that it
deserves. The usual methodology is to assume that pollution
emanates from a single source in the basic analysis, and when
the existence of many polluters is introduced, it is assumed,
as a simplifying measure, that the level of aggregate pollution
7
is equal to the unweighted sum of emissions from each polluter.
The additive assumption is not usually applicable to the phenom-
enon of aggregate noise disturbance. Moreover, the marginal con-
tribution of different noise emitters to the level of aggregate
noise disturbance, such as trucks versus automobiles, is almost
never equal. This is just to recognize that, today at least,
trucks are generally louder and thus more annoying than auto-
mobiles.
Logical efficiency criteria for the abatement of aggregate
noise disturbance should take these differences into account.
7. This assumption is explicit in Joseph J. Seneca and Michael
K. Taussig Environmental Economics, (Prentice-Hall, Inc.,
1974) p. 226; it is implicit in L.E. Ruff, "The Economic
Common Sense of Pollution," Public Interest, Vol. 19,
(Spring, 1970) reprinted in Robert Dorfman, ed., Economics
of the Environment, (W.W. Norton and Company Inc., 1972)
p. 13; it is probably implicit in Robert Dorfman,
Ibid., p. xxxviii.
80
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The criteria should provide a set of possibly different standards,
based on the relative contribution of different noise emitters, for
their joint abatement efforts. If trucks produce more of the ag-
gregate noise disturbance than automobiles, stricter standards ought
to be set for trucks than for automobiles. The additive assumption
fails to distinguish differences in the relative contribution of
different emitters, such as trucks and automobiles, and thus would
yield inappropriate standards if applied to a case where the rela-
tive contributions are not the same. One of the main results of
this chapter is to specify the appropriate criteria for joint abate-
ment efforts.
Unfortunately, nothing can be deduced from economic postulates
about the particular form of the relationship between aggregate
noise disturbance and different sources of noise; thus, its empiri-
cal form should be the subject of high priority study by sound en-
gineers and statisticians. In this chapter, we assume only that the
relationship is a function with nice properties, or at least that
it can be approximated by such a function. In the equation that
follows, the subscript "m" is used to distinguish aggregate noise
disturbance r , from the privately owned factors of production
denoted by r.(i=l,2,...,m), to be introduced in Section E. Let us
define the function Rm+D •'
(la) r , =aggregate noise disturbance at location p
_e
(Ib) r =disturbance emanating from noise emitter f at
m p location p
12 F
rm+p=Rm+p(rm+p'rm+p"-- '"
where p=l,2, . . . , P and
81
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The function R + is the aggregate noise disturbance production
function, but rather than using this awkward locution, let us
refer to R . as the aggregate noise disturbance function, or
even more simply, as the disturbance function. The disturbance
function is assumed to be differentiable and strictly concave
over a relevant region. The concavity assumption means we can
scale the function in such a way that the first partial derivatives
of the function R are diminishing. Whether or not the con-
cavity assumption agrees with reality should be one of the items
of concern for sound engineers. At this juncture, it seems rea-
sonable to suppose that an intensification of the noise disturbance
at a single source has a declining marginal impact on the level
of aggregate noise disturbance in terms of willingness-to-pay.
If the disturbance function is deterministic, then its
arguments, r , denote the noise emissions of every noise
emitter at location p, and there are F of them. By noise emission
is meant the physical sound level that emanates from a noise
emitter at location p. The noise emission of a motor vehicle
at location p at time t depends on, at least, vehicle type, its
mode of operation, state of repair, and physical
characteristics of the highway; these factors are either
constant or determined by the vehicle owner. However, the chain
of causation is interminable; even if it were realistic to
82
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suppose it were possible to keep track of what vehicles, in particular,
had been on location at any given time, it would still be impractical
to proceed with a deterministic methodology due to the complexity
of the factors on which noise emission depends.
To render the measurement problem tractable, aggregate noise
disturbance ?m+ should denote a density function over an appropriate
and generally accepted measure of aggregate noise disturbance. The
-to V
arguments of the disturbance function {r _, , r ,...,r ) then
m+p m+p m+p
become random variables denoting the characteristics of the noise
disturbance emanating from representative types of noise emitters
at location p, such as trucks, busses, automobiles and motorcyles.
The NCB can make its classification as coarse or as fine a
partition of the universe of noise emitters as it pleases. For
purposes of economic analysis, it is convenient to classify noise
emitters by profit maximizing units; that is, by firms. Classifica-
tion by firms is perhaps not as immediately appealing from the point
of view of the measurement problem as partition by major product
type, but if we make a simplifying definition, we can retain most
of the desireable measurement properties of the coarser partition.
We define all firms in our economy to be profit maximizing units
which produce a joint range of goods, including motor vehicles. If
a firm produces motor vehicles, we restrict its production to one
and only one of the product types, namely trucks, busses, automo-
biles and motorcycles. Thus, for our purposes, a GM truck division
and a GM automobile division are defined as distinct firms.
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Suppose there are a total of F distinct firms in our economy.
Given a classification of noise emitters by firms, the definition
of r . as a random variable induces a one-to-one relationship
m+p
between the F firms and the arguments of the disturbance function,
(rm+p'rm+p''*''rm+p^' for every location p=l,2,...,P. In cases
f
where firm f produces no motor vehicles, r =OJ Thus, most en-
tries of the disturbance function are zero.
It seems likely that noise disturbance of vehicles of type
f, r + , would be constructed by an appropriate transformation
of (1) a density function over a measure of noise emission (a
physical sound level) from vehicles of type f at any location
and in any mode of operation, (2) a density function over average
time spent on location p by vehicles of type f, (3) the clock
time on a 24-hour day (because of the periodicity of aggregate
noise disturbance), and (4) a density function over the number
of vehicles of type f in operation on location p during a typical
day. Factor (1) is determined by decisions of firm f, while fac-
tors (2) and (4) are determined by vehicle owners and operators.
Factors (2) and (4) also depend on the characteristics of location
p. In this chapter, we assume that factor (1), the density func-
tion over noise emission, is the only control variable for aggre-
gate noise abatement purposes.
We suspect that the relationship between density functions
over a measure of noise emissions from automobiles versus trucks,
for example, before noise abatement measures, is similar to the
relationship between the two curves shown in Figure (3.1-1). The
density function for automobile noise emission puts the weight
84
-------
density
db(A)
Figure 3.1-1. Before Noise Abatement
v density
db(A)
Figure 3.1-2. After Noise Abatement
85
-------
of noise emissions from automobiles to the left of trucks.
After noise abatement, the density functions are closer to-
gether and shifted to the left as shown in Figure 3.1-2.
Thus, a third property of aggregate noise disturbance, that it
emanates from many uncoordinated noise emitters, strongly suggests
that the appropriate measurement technique should be stochastic.
Indeed, such measures exist.
One such technique constructs a measure of aggregate noise
disturbance from the cumulative density function associated
with the density function R . The basic idea is that the
psychological experience of noise disturbance correlates
directly with the magnitude of the difference between the
background noise level and peak noise levels. The background
noise level is defined to be the decibel level that is exceeded
90% of the time in one day and the peak noise level is defined
to be the decibel level that is exceeded only 10% of the time,
these noise levels are given by the 10th and 90th fractiles,
respectively, of the cumulative density function associated
with VP-
As an example, the background noise level in a suburban
area might be 35 decibels with peak levels of 75 decibels.
This means 90% of the time the noise level exceeds 35 decibels,
but 75 decibels is exceeded only 10% of the time. The difference
g
of 40 decibels is used to measure the aggregate noise disturbance.
8. For a discussion of such measures, specifically the Traffic
Noise Index (TNI), refer to U.S. Environmental Protection
Agency, Community Noise, op.cit.. PP- 66-79.
86
-------
Henceforth, noise is always referred to in one of four
ways. Aggregate noise disturbance is a random variable Deferring
to the noise characteristics of a given geographic location; it
is the object of noise abatement activity. A noise emission refers to
(1) the sound emanating from a single noise emitter, or (2) a
density function over a measure of noise emission by emitter
type. The context shows whether (1) or (2) is intended. Noise
disturbance is a random variable denoting the noise characteristics
of representative types of noise emitters at a given location.
87
-------
C. Public Goods, Market Failure and Externalities.
The abatement of aggregate noise disturbance is a public
good. Thus, all who frequent the quieted location receive the
benefit of an equal magnitude of aggregate noise abatement
(although they may have different subjective valuations of the
same magnitude) and an addition to the magnitude of aggregate
noise abatement by any one individual implies no reduction in
the magnitude received by any other. The concept of a public
good is familiar and would seem to be the natural formulation
when those who jointly benefit are supposed, in principle, to
compensate the firms or consumers who jointly produce the benefit,
9
at cost to themselves.
We imagine the NCB levying a tax on those who frequent the
locations in its jurisdiction and benefit from aggregate noise
abatement. In the case of traffic noise, the NCB, as middleman,
supplies the efficient level of aggregate noise abatement to
individuals by offering to pay efficient prices to motor vehicle
manufacturing firms for the installation of improved noise control
systems on new vehicles. The NCB then collects just enough in
taxes from the residents and visitors of the area to cover the
cost of payments to the vehicle firms.
For the original statement of the theory of public goods,
Paul A Samuelson, "The Pure Theory of Public Expenditure,"
The Review of Economics and Statistics, Vol. XXXVI, (Nov.,
1954) pp. 387-389; and "Diagrammatic Exposition of a Theory
of Public Expenditure," Ibid., (Nov. 1955) pp. 350-356.
88
-------
The concept of a public good is closely associated with
the concept of market failure. Part of the "publicness" of
the public good is the fact that some form of collective action
is usually required to secure an efficient provision of the
good because the unaided market mechanism does not bring about
this result. It may be instructive to explain why the market
fails.
No production occurs if the industry supply price for
some commodity X is everywhere above the demand price. It is
often the case that the marginal cost of provision of a public
good is much greater than any one individual is willing to pay
by himself. This situation is pictured in Figure 3.2, which
represents an economy consisting of commodity X and two consumers ;f
A and B. The supply curve SS is the rising portion of the s
industry marginal cost curve. DD. and DDR are the demand ••'
curves of consumers A and B, respectively. I
If commodity X is a private good, the absence of production ,,<
is not the result of market failure; rather, the market functions '
i <'
properly because any production would be inefficient. To con- ;
trast this situation to the public good case, we observe that
a marginal unit of private good X cannot be jointly consumed
by A and B together; if A consumes the marginal unit, B cannot
consume it, and vice versa. Therefore, A's demand price for
10. Consumption is rival, see Richard A. Musgrave and Peggy B.
Musgrave, Public Finance in Theory and Practice, (McGraw
Hill, 1973), Chapter 3.
89
-------
K .
P
D
D .
0
Db
Figure 3.2. Supply and Demand for Commodity X.
90
-------
B's consumption is zero, and vice versa. There is no community
of interest with respect to X, and thus no incentive to pool
resources. Since the highest bid price (A's) is less than the
cost of producing even the first unit, production of X is zero.
If X is a public good, then both consume a marginal unit
equally and an addition to A's consumption implies no subtrac-
tion from B's consumption, and vice versa. In this case, A's
demand price for B's consumption is the same as his own, and
vice versa. The existence of a public good creates a community
of interest between A and B and there is a clear incentive to
pool resources. They should add respective marginal demand
prices for each additional unit of output of X. Together,
they may be able to cover the marginal cost of producing a
marginal unit which both would then consume equally, whereas
singly, neither could cover the marginal cost and consumption
would be zero.
Market failure occurs because in the general case of many
consumers, A and B would not likely know about each other's
demand prices without taking special actions to determine this
information. It seems clear that some form of collective
action is desirable to bring about the ideal results that
would follow from perfect knowledge of everyone's demand prices.
The joint (social) demand curve is shown by the curve EFDA-
The equilibrium level of output is OQ and the equilibrium price
is OP=QG+QH. The nature of the collective action required is
for everyone to inform eachother about their true demand
91
-------
prices and to make an arrangement to inform the producer of
their joint bid per unit of output.
The procedure which is usually envisioned for collecting
information on demand prices for public goods is a survey in
which consumers are asked for their "willingness-to-pay" for
a marginal unit of the public good. Thus, demand prices have
come to be called willingness-to-pay prices in works on public
goods theory.
An externality arises whenever the activities of some
firms or consumers impose uncompensated and involuntary costs
or benefits on other firms or consumers. The concept of a
public good seems to apply to the consumption side of human
activity, whereas the concept of externality seems to apply
to the production side. Aggregate noise disturbance is an
external diseconomy produced by both firms and consumers, but
its effects fall almost exclusively on consumers. Current evidence
suggests that in most cases noise does not affect the general level
of productivity;" indeed, it appears that,in some cases loud
noise boosts labor productivity. Therefore^we assume that
aggregate noise disturbance does not appear in the production
functions of firms; however, aggregate noise disturbance is
clearly a nuisance to individuals and should appear in their
utility functions.
11. U.S. Environmental Protection Agency, Public Health and
Welfare Criteria for Noise, op. cit., page 8-1.
92
-------
D. Consumers' Rights and Public Factors of Production.
If the NCB defines noise abatement as a public good, as
was done in Section C, it implicitly gives property rights to
producers in an artificial market set up and administered by
12
the NCB. The NCB requires consumers to pay the producers of
noise disturbance for contributions to aggregate noise abatement,
and acts as a collection agent for producers.
Alternatively, the NCB could give rights to consumers.
It declares a quiet environment as a natural resource to which
all consumers have joint ownership rights. Anyone who contri-
butes to aggregate noise disturbance is required to compensate
consumers for depletion of this jointly owned resource, and the
NCB acts as a collection agent for consumers who own this resource.
A public factor of production is defined as a public natural
resource possessed by all consumers in equal amount and to
which all consumers have joint ownership rights, such that each
individual's possession of the public factor implies no deple-
13
tion of the amount possessed by any other individual. Conversely,
a depletion of a given amount possessed by any one individual
implies an equal depletion of the amount possessed by every
other individual.
12. The terms "producers' rights" and "consumers' rights" as
applied in this context are due to David Starrett and Richard
Zeckhauser, "Treating External Diseconomies-Markets or Taxes?"
in John W. Pratt, Statistical and Mathematical Aspects of
Pollution Problems, (Dekker, N.Y., 1974.)
13. The definition of a public factor of production is adapted
from Paul A. Samuelson's definition of a public good, op. cit. ,
(Nov., 1954) p. 387.
93
-------
The previously introduced notation for aggregate noise
disturbance r denotes depletion of the public natural re-
source defined as a quiet environment at location p. Let the
"IP H
vector (r ,r . ,...>rm+D) denote the amounts of aggregate
noise disturbance depleted from the stock of quiet at location
p owned jointly by all the individuals 1 through H in our
economy. From the definition of a public factor, it follows
that r + =r1+ =rffl+ =. . .=rjj+ .
A careful study of the relative merits of consumers' rights
versus producers' rights is not presented in this chapter. We
assert that both cases determine efficient equilibrium levels
IJ< of aggregate noise abatement, but this does not mean that the
I, two alternatives are equivalent in other respects. For one
•i.;| thing, income distributions are different. If there are no
income effects, we conjecture, tentatively, that equilibrium
•^]; levels of aggregate noise abatement are the same in both cases.
'-• M »
The political and administrative problems of implementation of
('*: each are obviously quite different.
r;«' We assume, in this chapter, that the NCB decides to give
rights to consumers. If the disturbance R_+_ is deterministic,
then magnitude of aggregate noise disturbance r depends on
the physical noise emissions of vehicles owned by individuals
who can be named by personal or company name. It would be
natural for the NCB to levy a direct tax on each noise emitter
at a rate dependent on his or her noise emission r . . In the
94
-------
case of traffic noise, some noise emitters are profit maximizing
firms, such as trucking companies, and others are utility max-
imizing consumers who use privately owned vehicles for their
own convenience. To some, a system of direct taxation may seem
to have the virtue of fairness, but it makes massive demands on
the NCB's information system and requires a complex administrative
system for implementation.
If the disturbance function Rm+ is stochastic, then, as we
have seen, aggregate noise disturbance r depends on the noise
disturbance characteristics of different types of motor vehicles
classified by firms rather than the noise emissions of particular
motor vehicles owned by persons who can be named by name. Since,
by assumption, the control variable for aggregate noise abatement
purposes is the density function over noise emission by vehicle
type, a system of indirect taxation seems appropriate, determined,
say, on a state by state basis, and is less complex than the system
of direct taxation proposed for the deterministic case. The NCB's
for each state present tax bills to every firm f in an amount de-
termined statistically by the magnitude of noise disturbance r .
If r = 0, for all p, then firm f's tax bill is zero. This
system causes the firms whose products contribute to aggregate
noise disturbance to pay for contamination of the quiet environment
and provides an incentive for the installation of improved noise
emission control systems on new vehicles. Ultimately, the owner
of a particular vehicle pays for the additional cost of an improved
noise emission control system in the form of a higher purchase
price and probably higher operating and service costs.
95
-------
1)1.
i.C"
is:
IS •
if
if:
In the end, the direct and indirect tax systems place the
burden of payment on the owners of vehicles, and are equivalent
in this respect. It would appear that the system of indirect
taxation demands less information and is easier to administer
than the system of direct taxation. For this reason, we assume
that the NCB elects to implement the system of indirect taxation.
A tax on the firm that is ultimately paid for by the consumer is
called an excise tax.
96
-------
E. A Theorem on the Pricing of Aggregate Noise Disturbance.
We now turn to a general equilibrium analysis of the system
of motor vehicle noise disturbance excise taxation introduced
in Section D. The analysis yields a set of efficient tax rates.
The set of tax rates is to be interpreted as a set of efficient
unit prices per increment of expected value of noise disturbance,
Er . We assume that any given firm, referred to as firm f,
has significant control over the magnitude of Erm+p through its
ability to change the density function over the measure of noise
emission emanating from vehicles of type f. We assume that the
concrete form of this relationship is known to both firm f and
the NCB.
Let wf denote the price per increment of Er , . We
m+p m+p
understand that firm f is free to let Erm+ take on any value
that it pleases, provided it pays a daily amount equal to
wf* x Er* to the NCB.
m+p m+p
A Definition of the Economy
Let the economy consist of F firms, H individuals, n private
consumption goods, m private primary factors, and aggregate noise
disturbance at P different locations.
We respecify the disturbance function Rm as a density
function over the random variable rm+psuch that:
(2a) r = aggregate noise disturbance at location p;
97
-------
f
(2b) Er + = the expected value of noise disturbance of the type
m ^ of vehicle produced by firm f;
(2c) rm+p ' Vp(Erm+P'Erm+p'-••>*
where p=l,...,P,
'- 0, and > 0.
v m+p
The density function (2c) is assumed to be a stochastic, dif-
ferentiable production function for r + . In order to preserve
our Section B assumption of diminishing marginal returns, we
f
assume that the expected value function Er is strictly concave
over a relevant region.
In conformity with notational conventions and general
14
equilibrium methodology of standard economic textbooks, let
the following vectors denote the physical elements of the economy:
Vector Definition of Each Component
(3a) c = (c- ,Cr), . . . ,c ) private good j consumed by
individual h,
V^ i_ r. -L
(3b) r = (r -f,r " ...,r ) initial stock of private factor i
o 01 ot om owned by individual h,
i 1» Lt V»
(3c) r = (r1,r9,...,r ) private factor i supplied by
x * ra individual h,
14. James M. Henderson and Richard E Quandt, Microeconomic
Theory, (McGraw Hill, Inc., 1971) chapter 7; Michael D.
Intriligator, Mathematical Optimization and Economic
Theory, (Prentice - Hall Inc., 1971) chapters 8 and 9.
98
-------
Vector Component
(3d) r - (rm+1>rm+2>•••>rm+p)Public factor p (aggregate noise
disturbance at location p)
supplied by H individuals equally,
P=l,2,...,P;
f f f f
(3e) c = (c1 ,c0,•••,c ) quantity of private good j sold
1 ^ n by firm f,
f f f f
(3f) r = (r-,r2,...,r ) quantity of private factor
ra i purchased by firm f,
(3g) Er^ = (Er* 1}Er* ,... ,Er* )quantity of public factor p
p m+i m+<: m+f (expected value of noise
disturbance at location p)
purchased by firm f,
p=l,2,...,P.
With the understanding that; henceforth, components of Er are
expected values, we suppress the operators and write the vector
rf
P
'
Likewise, we suppress the operators in the disturbance function
rm+p and write
1 9 K
(2c J rra+p=Rm+p(rm+p'rm+2'- • ' >rm+p)-
The relevant price vectors are given by:
Vector Component
(4a) p = (P^Po, • • • ,Pn) price of private good j,
•"• ^ n H = 1 9 n1
J J- » ^ > • • • > li >
99
-------
Vector
(4b) w= (w1)w0,...,w )
-L & m
Component
price of private factor i,
_| _ -10 «*•
1=1,2 , . . . ,m,
TO U
(4c) wh = (wh ,wh ,...,wh )
P P P p
(4d) wh = (wh!?, whg, . . . ,whp)
p
(4e) wfp= (wfj,wf2,...,wf£)
(4f) wff= (wf* wf , . . . ,wfp)
p 2
selling price of every individual
h for location p aggregate noise
disturbance r + (location fixed,
p=l,2,.. .,P) h=l,2... .,H;
selling price of individual h for
location p aggregate noise distur
bance r (individual fixed
p=l,2,...,P
demand price of every firm f for
location p own noise disturbance
r £ (location fixed, p=l,2,...,P,)
demand price of firm f for location
p own noise disturbance r f (firm
fixed, f=l,2, . . . ,F,) p=l,2, . . . ,P.
The profits of all firms are summarized by the vector
(5) «= (if^fg,..., ^
We assume that individuals own shares in firms and that all profit
accruing to the firms is divided between the owners in proportional
shares. Let sf be the share of firm f owned by individual h. Then
ownership of firms by individual h is given by
(6)
H h
where z sf=l.
h=l
100
-------
We assume that the economy is competitive and that individuals
maximize utility functions U,
(7) Uh=Uh(ch,r£ - rh, -rp), h=l,2,...,H
15
subject to a real valued budget constraint
(8) w.rh+whp.r +sh. TT =p . ch , h=l,2,...,H.
We also assume that the total income recieved by individual h
from the sale of factors and share of profits of firms is spent
on goods and services.
Firms maximize real valued profit functions,
(9) * f=p.cf - w.rf - wf£ . r* f=l,2,...,F
A. }J ^J
subject to a production function
(10) Ff (cf;rf;rp) = 0 f=l,2,...,F.
In addition, we require that private markets are cleared,
H F
j c* - z
h=l J f=l
(11) j c - z cf = 0 j = l,2 ..... n
H , F
r ~
and recall that
15. Each term in equations (8) and (9) is the usual real valued,
inner product of vectors; for example,
'rh=Jl Wiri' and whp'
101
-------
Equation (7) is the utility function U, of individual h
and equation (10) is the firm's production function in implicit
form. Both (7) and (10) are assumed to be differentiable over
a relevant region; equation (7) has all positive first order
partial derivatives, the production function (10) has postive
first order partials for all outputs and negative first order
partials for all inputs; (7) and (10) possess negative definite
Hessian matricies of second order partial derivatives. The
negative definite condition on (7) implies that the set of all
commodity combinations which yield a utility level equal to or
greater than some fixed indifference hy.persurface U, form a
1 fi
closed, strictly convex point set. The negative definite
condition on (10) implies that the input-output combinations
defined by _, , f f f, ^ n form a closed, strictly convex
r £ (c , r , r ) £ u
-trt
point set. These stringent assumptions of strict convexity
:!f.••': everywhere are made for analytical purposes, in order to
5 !*'
f|jl'; guarantee the existence of a unique solution to the general
18
equilibrium problem.
«••«:,
<:!!!' In particular, the assumptions of strict convexity imply
PL,:;
that indifference curves for consumption goods in two dimensions
are convex for every individual h. For every firm f, all one-
16. James M. Henderson and Richard E. Quandt, Ibid., p.39.
17. Ibid.. p. 97.
18. Ibid.. p. 189
102
-------
output production functions obtained by fixing the values of the
other (n-1) outputs are strictly conc.ave, and all one-input pro-
duction functions obtained by fixing the values of the other
(m+P - 1) inputs will be strictly convex.
The initial stock associated with the public factor r is
included in the utility function Uh as zero. A zero entry denotes
an absence of aggregate noise disturbance. We take zero aggre-
gate noise disturbance, or at least a noise level that is hardly
ever, if at all, annoying, as a benchmark corresponding to the
vector r .
o
Statement of the Price Theorem
A basic theorem in general equilibrium analysis is that for
a competitive economy in which there are n private goods and m
private factors, and in which individual utility and production
functions have properties implying strict convexity everywhere,
as assumed in this chapter, then there exists a unique set of
prices and wages such that (loosely speaking) the value of each
private good in consumption is equal to or greater than its
20
opportunity costs of provision in alternative uses of resources.
We assume that a pure, competitive equilibrium exists in the
private goods and factor markets of our economy. This means that
if there are no public factors to consider, then price vectors p
19. Ibid,. p. 97
20. Discussions of the general equilibrium problem may be found in
James M. Henderson and Richard E. Quandt, Ibid., pp. 189-190;
Michael D. Intrilegato.r, oP-. it., PP 238-241; Gerard Debreu,
Theory of Value, (Wiley,
103
-------
and w, given by definitions (4a) and (4b), exist and are unique.
Therefore, all that we must do to solve the general equilibrium
problem, given the existence of a vector of public factors r in
an otherwise purely competitive economy, is to exhibit a set of
prices that are consistent with equations and definitions
(2) through (12), less (4), and show that these prices exist and
are unique. In particular, we want the prices of aggregate noise
disturbance to be consistent with utility mazimization by individ-
uals and profit maximization by firms. The prices we want to
exhibit are those which the NCB should post in order to guarantee
an equilibrium.
••„, If NCB does not exist, or does nothing, an equilibrium exists,
,,(! '
'-• • nevertheless, in private markets. However, an equilibrium that
'! does not include positive prices for the public factor of noise
!|" .,
' V •' '
""'• disturbance is not efficient, as we shall demonstrate.
MI j
•f, A necessary condition for an economic optimium is that the
3'!;; 21
V'^"\ economy is in a state of Pareto efficiency. A Pareto efficient
state is an economic situation in which no feasible reallocation
<*:, ;
ill''; of physical resources would increase the level of utility of any
*:„ i
individual without lowering the level of utility of at least one
other individual. An economic optimium is necessarily Pareto
efficient since otherwise some individual can be made better off
without making any others worse off, a redistribution which is
clearly an improvement. Consequently, we want the selling prices
given in (4c) and the demand prices given in (4e) to be consistent
with a Pareto efficient state.
21. Michael D. Intriligator, op. cit., pp. 258-259.
104
-------
Selling prices for a public factor correspond to willingness-
to-pay prices in the analysis of public goods. The selling prices
monetize the marginal costs imposed on individuals by an increment
to aggregate noise disturbance r . To allow for noise averting
behavior, we assume that selling prices are those demanded by
individuals after optimal noise averting actions have been taken.22
We assume that the NCB has perfect knowlege of the relevant
selling prices, obtained, say by means of a survey. Selling
prices are given by the vector wh in definition (4c). The
components of wh denote the marginal costs to individuals h=l,2,
...,H for an increment to r + • In other words, the component wh
could be interpreted as a bribe denoting the amount of money
required by individual h in order to be indifferent between no
increment to r and no bribe, and an increment to r . with a
m+p m+p
bribe and the opportunity to engage in averting activities. The
set of all such amounts for all possible levels of r . forms the
m+p
supply function of individual h for r , as shown in Figure 3.3.
wh£
rm+ p
Figure 3.3 Supply Function of Individual h for Aggregate Noise
Disturbance r .
22. The Efficient Outcome with Noise Averting Activities is
discussed in Chapter 2 of this report.
105
-------
We have assumed that 3 U /3 (-r )> 0 for all r > 0
IT m+p' m+p
Hence, 3UR/ 3r > 0, and it follows that dwhh/dr + >0 (if this
m+p
derivative exists). This condition is consistent with the rising
23
slope of the SS curve in Figure 3.3. 'We assume that the NCB
obtains perfect information on the selling prices wh of every
individual for each possible level of the components of r .
P
We now collect assumptions and state the following
Price Theorem Given selling prices wh =(whp,wh^ ,...,whH) of indivi-
duals for aggregate noise disturbance r at location p, there
exists a set of demand prices of firms for input rights to noise
f 1 ? T"1
disturbance r , denoted by the vector wf =(wf ,wf ,...,wf ).
it:
AS'
•' R .
• jl
ii"
23. It must be noted that nonconvexities probably exist. The
requirement 3UQ/3 rm+ 0 means increasing disutility obtains
for all
it is likely that 3U /3r
However, for r greater than some value,
(1) the
+ >0 for two reasons:
individual can leave location p if it gets too loud for him,
or (2) he may get saturated and not care about increasing
noise disturbance above a certain level. In case (1), Figure
3.3 would look like (a), while case (2) could have the shape
shown in (b).
(a)
m+p
Cb)
m+p
On non-convexitieg, see David Starrett and Richard Zeckhause-r,
op. cit., pp. 72=75 and p. 80; and William J. Baumol, "On
Taxation and the Control of Externalities", American Economic
Review. Vol. 62, (June, 1972), p. 317.
106
-------
The components of wh and wf are related by the formula
P P
(13)
$
H
Z
h=l
wh
f=l,2', ... ,F
'm+p
Equation (13) defines wf for every f and every p. The vector
wf is the only set of demand prices consistent with the require-
ments (a) firms maximize profits, (b) individuals maximize utility,
and (c) the allocation of resources is Pareto efficient.
Corollary Resource allocation in competive markets is Pareto
efficient only if equation (13) is satisfied.
Equation (13) requires that the per unit price paid by firm f
j
for own noise disturbance r , at location p is equal to
m+p
summed individual supply
prices for aggregate
noise disturbance r .
marginal product of firm's
own noise disturbance r^+
in the production of m
aggregate noise disturbance,
107
-------
F. Proofs of the Price Theorem and its Corollary
A proof of the price theorem proceeds from the assumption
that requirements (a), (b) and (c) hold, along with equations
and definitions (2) through (12). First, a Pareto efficiency
criterion for public factor markets covering the allocation of
aggregate noise disturbance rm is deduced. Second, we exhibit
necessary first-order conditions for maximum utility and maxi-
mum profit, then equation (13) follows easily from the first-
order conditions and the Pareto efficiency criterion. Third,
the corollary is proved.
';;• A Pareto Efficiency Criterion
,f ] From the definition of Pareto efficiency given in Section
'.'.r
'I" '
•J;; • E, it follows that a necessary and sufficient condition for a
• t
,t Pareto efficient economic state is that an arbitrary individual
• *•'
!p h maximizes utility subject to the (F + P + n + m) constraints
•'<> 1
given by (10), (2c') (11), and (12) and the (H-l) fixed utility
'*;•; levels U , q=l,2,...,H, qfh. To deduce necessary conditions
k'"i. for Pareto efficiency, it is sufficient to maximize the utility
level of an arbitrary individual, say h=l, subject to the above
constraints. Form the Lagrangian Z:
H F n F f
(14) Z=U- + i Xh(U, - U. ) + z 9. Ff + E a ( E c, -
1 h=2 " n° f=l j=l J f=l J
/%"/ 4- f n ( r- y*1 _ ^ T \ 4- v f ( f — R
108
-------
The relevant first order necessary conditions for a maximum are
, Z , U,
(15a) 9-_= - ' !
3rl 3rl + 0i = 0 i=l,2,...,m
3 Z 3 U,
(15b) —r~ = - *h —g- + fj = 0 h=2,3,...,H
O T* 0 T» i "t O
1 -i T i 1-1,
-------
r for the i... private factor r. is equal to the weighted rate
of technical substitution of every firm of own noise disturbance
f f
rm+p for the firm's use of the i-th Private factor r±, where the
weight is, in each case^the reciprocal of the marginal product
of r in the production of rm+D- Since (16) is a necessary
condition for Pareto efficiency, requirement (c) of the price
theorem holds only if (16) holds.
To show (16), rewrite (15d) as
3U1 H 3U.
(17a) -1 + t * h _
h=2
,*' Equation (15e) implies
it; !.
(17b)
p
Thus, substituting (17b) in (17a) yields
9U1 H 3\ 9
(17c) _L_ + Z h_Jl_ = 9
Now from (15b) and (15c),
i
and
x h ' V ^
Bi
(17e) 9 f =
Substitution of (17d) and (17e) in (17c) yields
_
3rm+p h=2
110
-------
but (15a) shows
9U
(17g) B..
Divide both sides of (17f) by B., and substitute elL/ar for
$. to obtain
(17h)
Now (17h) holds for every f=l,2,...,F. The left hand sides of
all such equations, for a fixed i, are equal. Thus, by
transitivity, the right hand sides are all equal. This completes
a proof of equation (16).
f
A Proof of the Existence and Uniqueness of wf .
We now assume that requirements (a), (b), and (c) hold;
profit maximization conditions are given by equations (9) and
(10). We form the Lagrangian
(18) Q=p.cf- w.rf - wf* .Tp + vfFf f=l,2,...,F.
Relevant first-order necessary conditions are given by
3Q 3F
(19a) —j- = - Wj, + vf j- = 0 1=1,2, . . . ,m and f=l,2, . . . ,F;
3ri 3ri
8. = - wff * v = ° P=1.2.--"P and f-l,2,...,F.
f wi vf f
3 rm+p 9rm+p
111
-------
Utility maximizing conditions are given by equations (7) and
(8). We form the Lagrangian
(20) M=Uh + yh(w.rh + whp.r + sh. n - p.ch)
relevant first-order necessary conditions are
3M au.
(21a) r- = g- + y w. = 0 1=1,2, . . . ,m and h=l,2, . . . ,H;
3r" 3r" n
3 M 3 U .
(21b) = + y wh" = 0 p=l,2, . . . ,P and h=l,2, . . . ,H.
^ f 5 T> '1 P
d m+p d m+p
•». , We assume that other first-order and the second order conditions for
ir •*.
'*'•;:: a maximum are satisfied.
•-'»; • Inspection of the profit functions (9) and budget constraints
"' ' (8) shows that multiplication of both sides of (9) and (8) by a
!»••!; scalar does not change the equilibrium solution. Thus, all
IV ••
i'C'}- supply and demand functions are homogeneous of degree zero in
all prices, and we are free to choose a numeraire. Define the
(»! ] i,, private factor as numeriare; we set w.=l. From (19a) and
|: t L/ il J-
(19b) we obtain by division,
3F^/»r^._ wf* f n_i o n
,00v f' m+p p _ ,..fi p-1,2, . . . ,P
(22) 3—•=— K wi
3Ff/arJ WjL P f=l,2,...,F
and from (21a) and 21b), we obtain
h
112
-------
Now requirement (c) implies equation (16) which states
From (22) substitute wf on the right-hand side of (16) and cross
multiply by 9Rm+p/ ar m+p to obtain
(24) ZH 3 V 3rm+p 3Vp _ f
I—"" i l~ -P " -^ *
h=1 3UK/9rh Sr^ P
h' i m+p
If (23) is multiplied on both sides by gR +D/9r + , we get
- =wh for h-l,
For each h=l,2,...,H, substitute the right hand side of (25) for
the h., term of the sum on the left hand side of (24). This yields
tn
H 3R« f=l,2, . . . ,F
,- - P P-1.2 ..... P,
h~i
as desired. This proves that equation (13) holds if (a) firms
maximize profits, (b) individuals maximize utility, and (c) the
allocation of resources is Pareto efficient. By assumption the
~\ 9 IT
vector wh =(wh , wh ,..., wh ) exists; hence, the existence and
uniqueness of each wf is guaranteed by equation (13).
113
-------
A Proof of the Corollary.
Assume that resources are allocated in competitive markets,
and assume that all public and private markets are in equilibrium.
This equilibrium is a possible candidate for Pareto efficiency,
since it is well known that a competitive equilibrium in private
markets satisfies some necessary conditions for Pareto efficiency.
Now suppose that the equilibrium jjs Pareto efficient. We show
that a contradiction results if we also suppose that equation
(13) is not satisfied. The inconsistency of these two supposi-
tions proves that a competitive equilibrium is Pareto efficient
only if equation (13) is satisfied.
'•*-.
. ' r
w'
j£ !; The price theorem states that requirements (a), (b) and
=»•:•;;
(f ' (c) together imply equation (13); the contrapositive of this
',;;!; implication requires that if equation (13) is not satisfied,
'• * • •. •
•j ;, then at least one of the three requirements is not satisfied.
IV ''
,(<• , But the analysis of pure competition shows that failure of
• »> *',
i either requirement (a) or (b) is sufficient to guarantee
failure of requirement (c). This proves that equation (13)
is a necessary condition for Pareto efficiency.
We observe that equation (13) is not sufficient for
Pareto efficiency; for example, if private markets are not
in a state of competitive equilibrium, then the economy is
not in a Pareto efficient state. Either both partial equili-
briums in private and public markets are Pareto efficient, or
neither is Pareto efficient.
114
-------
If an economic state is Pareto efficient, we say that the
economy is efficient. We note that we did not have to assume
the existence of competitive markets in order to prove the price
theorem.
115
-------
G. Interpretation of the Price Theorem.
Equality of Cost and Benefit of r .
An efficient economic state implies that the marginal cost
and benefit of aggregate noise disturbance are equal. Consider
equation (16),
H »u /:
(16) s —2—
On the left hand side, we have the marginal cost of an increment
to aggregate noise disturbance r _ (MC ). That is, using (23),
»' •"
l „«* " 'V r°*P H
(26> h-£i 3T^ = £1 »»P - "V
»•:
al -*
•"•'" "1 9 TT
j ,.' The vector wh = (wh , wh , . . . , wh ) denotes the selling prices
:»,' , of individuals for an increment to r . The sum of such selling
^
prices is the marginal cost to society for an increment of
aggregate noise abatement rm+p- We now show that the right si
of (16) denotes the marginal benefit to society for increments
to r . From first order conditions for competitive profit
m+p
maximization, it is easy to deduce the condition
PJ
or taking the absolute value of the two right-most expressions,
3 c. • wf
(.27) —$ = 'm*J - P
rm+p
116
-------
The magnitude of the partial derivative »c./3r + if it exists
f
is interpreted as the marginal product of r + in the production
of an arbitrary private good, c.. Thus
(28) wf* = p MPf;j.
tr J r
Equation (28) shows that firm f 's profit maximizing demand price
per unit of r is equal to the value of the marginal product of
his own noise disturbance r + in the production of c . . To obtain
the value of the marginal product of aggregate noise disturbance
r +D in "the production of c . , we have to distribute p. MPf over
f
the increment to r + that results from a unit increment to r .
This is done by dividing p. MPf1^ by 3 Rm+p/8 '• that is
(29,
The middle expression of equation (29) is the marginal benifit
of an increment of aggregate noise disturbance rm produced by
f
firm f (MB ). Using equations (22) and (29), we can write
Equation (30) is valid for all firms f=l,2,...,P. Equations
(16), (26), and (30) demonstrate that in a competitive equilibrium,
the marginal cost of an increment of r-m+p, denoted MCp, just equals
117
-------
the marginal benefit of its use in production by an arbitrary
firm, denoted by MB ; thus, we have MC =MB for all f=l,2,...,F.
12 F
By transitivity, MB =MB =...=MP . This shows that the marginal
cost of aggregate noise disturbance everywhere just equals the
marginal benefit of its use in production by firms. This result
is the usual result obtained in the theory of public goods.
Price Differentiation and Own Noise Disturbance
A consequence of the price theorem is that efficient unit
prices paid by different firms to the NCB for rights to use own
noise disturbance are equal in a competitive equilibrium only if
'£;, different firms produce the same aggregate noise disturbance. That is
ib
,,.,-<» f e
', *< (31a) wf = wf° if and only if
*.».• •; t*
*•'•'•' a'R aR
9 m+p _ 3
/ o-i "u \ U1
(31b) — f
e
. -. 3r 8rg
:",. m+p m+p
fch-
3 where g ^ f , g,f=l,2,. . . ,P.
MR:!!?
p-^ Equality (31b) holds in special cases. An example of a
24. For example, "the broad productivity criterion requires that
emissions be controlled in such a way that the marginal cost
of further reductions be the same for all sources of pollu-
tion". Robert Dorfman, op.cit. , p xxxvii. Also "Once cost
and benefit functions are known,the PCB [Pollution Control
Board]] should choose a level of abatement that maximizes
net gain. This occurs where the marginal cost of further
abatement just equals the marginal benefit". L.E. Ruff,
reprinted in Ibid., p 11.
118
-------
special case where equality (31b) holds is when the disturbance
function Rm+ is an unweighted sum of its arguments
12 F 1 2 P
(32) rm+p=Rm+p(rm+p'rm+p rm+p) = rm+p+ rm+p+ '''+ rm+p'
In Section B, we saw why this function which, for the sake of
simplicity, is often assumed in the many-polluter case, does
not usually characterize the phenomenon of aggregate noise
disturbance.
The possibility of unequal unit prices for noise disturbance
is perhaps counter to expectations because the familiar analysis
of pure competition shows that all firms pay the same price for use
of factors of the same type. Among the assumptions which lead to
the usual results are that private factors are identical, there
are many sellers of private factors, and exit and entry into the
market is free.
In the case of a public factor, such as noise disturbance,
it seems reasonable to keep the latter two assumptions. Many
firms and sellers take part in the artificial market set up by
the NCB, and entry and exit into the market is free. However,
the noise disturbances of individual firms such as r^+p and
rf+ , gff, are not generally identical in the sense that, unless
3R /3r* = 8R . /3rB. , increments to r* and r? result in
m+p' m+p m+p' m+p' m+p m+p
different increments to aggregate noise abatement rm+p. Since
it is aggregate noise disturbance rm which enters the utility
119
-------
functions of individuals directly, the theoretically correct
valuation of r . depends on the increment to r which results
m+p m+p
f
from an increment to r . This increment is given by the
f f
function 3 Rm+D/ ^m+n and depends on the absolute level of r D-
For any individual, the marginal cost of an increment to r
is given by wh , a price which depends on the absolute level
of r + . Hence, the correct cost to this individual of an
increment to r is given by n
_.
P 3rf
m+p
The sum of all such valuations over every individual gives the
f
t marginal cost of an increment to r . This is the sum that
»?r '
(Cl. is defined in equation (13).
'«;-q
if' it This discussion shows that prices paid by firms for own
C»'
«-•-•• noise disturbance, given by equation (13), need not be equal.
* * ";
I? ' l\ However, the price paid by the firm for an increment to aggre-
$' "
|i" jj gate noise disturbance is equal for every firm.
Zero Profits and the NCB
If the NCB does not make a profit, then total payments
received from firms must equal total payments to individuals
by the NCB. This condition is given by the sum of scalar products,
120
-------
P F
(33) v w^ rM__ = E E wf r
p=l f=l P
H
where w = 5- wh
P p
h=l
But wfp is given by the sum of scalar products
j? n. , DK
P P 3rf p 3vf
h=l drm+p 9 rm+p
Thus, (33) can be rewritten as
p P F
V W T* =r r r*
z p m+p E z
p=l p=l f=l "im+p
(34) i w r = i r w "?+P— f
1 p m+p *• L wps f rm+p
P F 3R
2 t wp rm+p¥~f
p=l f=l m+p
Dividing both sides of (34) by the scalar w yields,
P P F „ 9 R .
^ - f m+P
-
p=l p=l f=l m+p
Equation (35) can be interpreted to mean that the requirement of
zero profits and efficient pricing for the NCB implies that in equili-
brium the sum of aggregate noise disturbance over all locations
p=l,2,...,P is a weighted sum of noise disturbance rm of
every firm f=l,2,...,F at every location p=l,2,...,P. The
weights are the respective marginal products of each noise
f
disturbance r in the production of aggregate noise
121
-------
'tf> <,"
'»! * -•
disturbance rm+ . The sum on the left of (35) is, obviously, a
measure of economy-wide aggregate noise disturbance.
We shall now demonstrate that if all profits accruing to firms
are divided between individuals, then equation (33) is satisfied.
First, we sum all the real valued budget constraints over h=l,2,...,H;
this yields the real valued equation
H H H H TT
(36) w.( E Th Z r!;,..., E. rjj) + < E wh^.E whj, . . . ,
h=l l h=l ^ h=l m h=l i h*l ^
H, HhH H H H
E wh ). r + ( E s" z. s° ..., z s"). n= p.( z c z c9, . .. ,
h=l P p h=l X h=l 2 h=l * r=l "h=l 2
H
E c ).
h=l n
Let us define
a.u H h F f
a,:; (37a) c,= E c" = E c* j = l,2,...,n
Jrix- J h=l J f=l J
ii H , F f
,.r j (37b) r.= E r.= E r. i=l,2,...,m.
ijiJ:; h=i f=i x
*• *• H
Recall the definition of w in (33) and that E s^=l from (6),
p h=l
and using (37), write (36) as
(38) w.(r1,r2,...,rm) + (w1,w2,. . . ,wp).r + (1,1,...,!). TT
= p. (c1,c2,...,cn),
Now the inner product of vectors (1,1,...,!). T yields the scalar
F
sum E rcf. Using equation (9) we write the real valued equation
f=l
122
-------
F F F F F F
(39) z *f=p.( Z c{, £ c2,..., z cn)-w.( Z ri> E rf
f=l f=l f=l f=JL f=l f=l 2
V F
f f f
j r )- E (wf .r ),
f=l f=l P P
or using (37a) and (37b),
F F
(40) £ Trf=p.(c1,c2,...,cn)-w.(r1,r2l...,rm)- E .
f=l f=l
F
Now substitute the right hand side of (40) for £ TVf in (38)
f=l
and cancel like terms: this gives
F
(41) (w w .,w ).r - Z (wr\O=0.
i ^ ^ p _ p p
Taking the indicated inner products of vectors and transposing yields
P F P
(42) * wp rm+p = E 2 wfp rm+p-
p=l p=l f=l
Since the terms of the sum on the right hand side are commutative
scalar products, we may write equation (42) as
P P F
(33) E w r . = z z wff r f
' p m+p p m+p
p=l p=l f=l
This shows that equation (33) is always satisfied if profits are
divided among individuals.
The Pareto Equivalence of Producers' Rights and Consumers' Rights
In Section D, it was asserted that producers' rights and
consumers' rights both determine efficient equilibrium levels of
aggregate noise abatement. We adopted the consumers' rights
case and implicitly chose a level of zero aggregate noise
123
-------
disturbance as a benchmark from which the magnitude of r
m+p
is measured.
We now examine the producers' rights position. Individuals
have to pay for the noise abatement activity of firms. We
define aggregate noise abatement as a public good. Suppose
we have an aggregate noise abatement function C ,
(43a) c + =aggregate noise abatement at location p
(43b) c + =noise abatement of firm f at location p,
(430
*!''". where p=l,2, . . . ,P.
««.•;$
Cli: The abatement function C + is assumed to have all of the
*••*"• nice properties of the disturbance function R , given by
>'*;);, equation (2cx). Implicit in this definition is the assumption
(}•—
fH|Jj" that a measurement of noise abatement activity by firm f is
' meaningful. This implies that the level of noise disturbance
»«;:$
IJll'k that would be produced by firm f in the absence of NCB regula-
FfeL
tory action is known as a benchmark from which the level of
f
noise abatement c , is measured. Let the benchmark be denoted
m+p
by N* Thus,
(44)
f f
N is a constant. In equation (44), r may be interpreted
f
both as the difference between the benchmark N and the firm's
124
-------
noise abatement activity c , and as the firm's use of noise
disturbance rights. In a producers' rights scheme, r is the
residual, while in a consumers' rights scheme, the firm purchases
rm+p' and cn+p is the residual-
We combine the disturbance function R , and the abatement
m+p
function C to define a benchmark for the level of aggregate
noise disturbance in the absence of an artificial market.
(45) RmVrm+p>rm+p> ' ' ' 'rm+P>+(Wcn+P' °n+p' ' ' ''Cn+p)
Since N is constant for all f, N is also a constant.
Utility and production functions are re-defined to be
consistent with producers' rights. Thus, (7) becomes
f4.fi"! Tl •=•( c* -r •-r --r \ h = 1 9 H
^ *±U ) U, — \ \-i , \-r , JL —J. ^ II .1 , <5 , . . . , -l-L
where cp =(cn+1,cn+2,-..,cn+p).
and (10) becomes
(47) Ff(cf;cp;rf)=0 f=l,2,...,F
where c=(c^,-, , c , 0 , . . . , c_
From equations (44) and (45), it follows that
(48)
n+p
125
-------
;>.=
<*••;••
f f f
because 9N /3r + = 0 and 3cn+D/8r +D= -1• Likewise,
f
a F ftF a \ 3 U. _ h d m+p _ d h
(50) h = • £— = -
3°n+p 8 m+p dcn+p ^m+p
Since /= 3r/3c= -1.
A Pareto efficiency criterion for the public factor market
is given by equation (16). We now derive a Pareto efficiency
criterion for the public goods market from equation (16). Use
(50) on the left hand side of (16):
€C
*""" H 3U,/3r . H 3U./3C ^ . . 0
*"vr*' (51) r h m+p _ _ h' n+p i=l,2,...,m
*»• l»i
* Likewise, use (49) and (48) on the right hand side of (16) to
C'lv obtain
kk ^ , f w , f
(52) -^/3^P 1 ._!V!!n±p 1
f* -P -F S S -F
/I •*-. / J. 0—, /oj.
/<\7» »\K /^T* *\ p / <\ T* C^ /P
/d T o^rrtj-T-,/ o -"-mj.!-! d *• ft d-1 ^ n+p n+p
for 1=1,2, . . . ,mj p=l,2, ...,]?.
Together, equations (16), (51) and (52) imply
(53) ?'V
126
-------
It will be stated without proof that the corresponding Pareto
efficiency criterion for the public goods market derived from
(46), (47) and appropriate profit and budget equations (derived
using the methodology of Section F), is given by
H 3U, /3c . 3F./3
f*a\ T h n+p _ f'
(54) I ^-^
h=l SU, / 3r . 3 f ^/3
Conversely, it can be shown, by the reader, that equations (54),
(51) and (52) imply equation (16), except for a sign change.
Hence, except for a sign change and given (51) and (52), the
criterion for Pareto efficiency in the public factor market
is satisfied if and only if the criterion for Pareto efficiency
in the public goods market is satisfied. The sign change can
be interpreted to mean that the criteria are mutually exclusive,
in the sense that one and only one holds, but either yields
Pareto efficiency. Thus, consumers' rights and producers'
rights are equivalent with respect to Pareto efficiency, but
a choice has to be made between then.
The sign change results from a change in the flow of costs
and benefits determined by the choice between consumers' rights
and producers' rights. In the case of consumers' rights
aggregate noise disturbance rm is a social cost, and thus,
the left hand side of (16) denotes the marginal cost (MC ) of
r , , while in the producers' rights case, aggregate noise
abatement c . is a social benefit, and thus the left hand side
n+p
127
-------
of (54) is the marginal benefit (MB ) of c + . In the former
case, costs flow to the individual because r , is produced,
m+p r '
while in the latter case, benefits flow to the individual be-
cause c + is produced.
The equilibrium interpretation of equation (54) is that
the sum of the marginal rates of substitution of every indivi-
dual (MRS, ) of cn for an arbitrary private factor (taken as
numeraire) denotes the marginal benefit to society of an in-
crement to cn (MB ); the right hand side of (54) denotes
25
the firm's marginal cost of producing an increment to
aggregate noise abatement c + , in terms of the i.. private
VN factor. Since (54) holds for all f=l,2,...,F, we have MB =
JrjJ MCf for all f, and thus, MC =MC1=. . . =MCF. This shows that
lU»! the marginal benefit of aggregate noise abatement everywhere
is**
*""*" just equals its marginal cost of production. In other words,
*• .•»,
•«•)»( if the Pareto efficiency criterion (54) holds, then the
!>• »«•.
l«k! following equality is satisfied,
8 H
*'% (56) MB = I MRS =MC .
CU P h=l h P
u,
We now show that the price to be paid firms for a unit
f
of noise abatement is just the negative of wf , as defined
in equation (13). The negative sign means that the direction
of flow of payment has changed from firm-to-individual to
25. Compare this interpretation of left and right hand sides
of (54) to the interpretation of left and right hand sides
of (16) given in this Section, Equality of Cost and Benefit
of r , .
m+p
128
-------
individual-to-firm (via the NCB) . Combining (51) and (23)
gives
H 3U,/3c . H ,
(57) I ~Jl - £±E = - I whh .
h=l 9Uh/3r^ h=l P
This means that the sum of willingness-to-pay prices over all
individuals for an increment to c is equal to the negative
of the sum of their selling prices for rm+ . Take the negative
of equation (13), and use the equality in (48) to write
In view of (57), equation (58) may be interpreted to mean that
f
the efficient price for firm f's noise abatement c . is equal
n+p ^
to the product
summed individual willingness-to-pay marginal product of
prices for aggregate noise x firm's own noise
abatement c abatement c* in the
n P production oPaggregate
noise abatement.
The theoretical equality of the magnitudes of the price
paid to firms for noise abatement and the price paid by firms
for noise disturbance suggests a procedure for testing the
accuracy of willingness-to-pay estimates inferred from random
sample survey data. Two different surveys should be adminis-
tered by the NCB to two different random samples drawn from
the target population. The first survey should be designed
to elicit data on willingness-to-pay for aggregate noise
abatement. The second should be designed to elicit data on
supply prices for aggregate noise disturbance. Separate
estimates of summed willingness-to-pay and summed selling prices
129
-------
for the target population should be inferred from the data of
the two surveys. Theoretically, the difference between the
magnitudes of the two estimates should be zero. If an actual
nonzero difference results, greater than what would occur by
chance, then either (1) the theory presented in this chapter
is false, or (2) better survey measures should be devised.
However, if the difference is less than what could occur by
chance, then the NCB can be reasonably sure that its estimate
of summed willingness-to-pay is a good one.
f
Computation of wf and the Information Demand.
Inspection of equation (13) shows that the NCB must have
complete information on the disturbance function R , in-
cluding information on the form of all first partial deriva-
f f
tives in order to compute wf . The first partials 8R + / 3r ,
in turn, are functions depending on absolute magnitudes of r +p,
for all f=l,2,...,F. The NCB must, therefore, compute efficient
levels of r for every firm f. This task makes heavy demands
on the NCB's information system.
For example, if production functions are nicely behaved,
and known to the NCB for all goods and all firms, the NCB can
compute the required levels of r_\ for all firms. We saw in
equations(28) and (27) that
f J 8 ° 3
rm+p
130
-------
The partial derivative 3c. /3rm+p is derived from the production
function of firm f, say
(59) cj=gf(rf ; /)
f f
Where r is given by definition (3f) and r , by (3g«). Thus,
(28) can be written
f 8gf
(60) wO»p.« - 1 -
r
m+p
Dividing both sides by 9 Rm+D/ 8r +D gives
5R / r -
3Rm+p/9rm+p
f
where h,. is a function of all r , f=l,2,...,F.
Equation (61) yields a system of F equations in F unknowns.
If the Jacobian of this system is nonvanishing, then we can
solve the system of F equations
f -
(62) rm+p=hf (wp> for f=l.2"-"
since the nonvanishing Jacobian guarantees the existence of
hf. Therefore, the NCB must have prior knowlege of the F production
functions g. defined in (59), in addition to the function Rm4.
131
-------
H. Conclusion.
The objective of this chapter is to determine efficiency
criteria for the abatement of aggregate noise disturbance emana-
ting from many sources. The findings are consistent with the
general criterion: the efficient level of aggregate noise abate-
ment is such that the marginal benefit of its provision is just
equal to the marginal cost of its production.
A variety of noise control strategies are available which
promise to implement this criterion. Among them are tax/subsidy
schemes and direct regulation of noise emission levels. This
chapter analyzes an excise tax system on the manufacturers of
motor vehicles. It appears that this strategy of control mini-
mizes demands on the administrative and information systems
required for implementation. If an excise tax system is adopted,
the responsible authorities should tax each firm, at a rate per
unit of noise disturbance equal to the product
summed individual supply marginal product of firm's
prices for aggregate noise x own noise disturbance rf+ in
disturbance r the production of aggregate
P noise disturbance.
It is shown in this chapter that these are the only rates,
compatible with a competitive system, which equalize marginal
benefit and marginal cost. Implementation of these tax rates
means that different firms would pay prices for noise dis-
turbance that reflect the contribution of each to the aggregate
level of noise disturbance. It is also shown that no competitive
price system is efficient unless these rates are charged for
noise disturbance.
132
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The information demands of an excise tax system are
limited to (1) determination of the fioise disturbance func-
tion and/or the noise abatement function, (2) the selling
price of every individual for aggregate noise disturbance
and/or the willingness-to-pay of every individual for aggregate
noise abatement, and (3) the production function of every firm.
The term "limited" is used to describe these demands only to
contrast them to the demands made by other noise emission con-
trol schemes. The measurement problems associated with the
gathering of the three blocks of information just listed are
very great. However, the theory described herein guarantees
that if this data can be collected, it can be interpreted and
utilized in a socially meaningful way. This theory should serve
to focus current information gathering activities aimed at under-
standing the aggregate noise disturbance phenomenon.
Finally, an hypothesis concerning the equality of summed
willingness-to-pay prices and summed selling prices is posed.
Estimates of these two magnitudes for the target population
should be inferred from data of different random surveys designed
to elicit each. The likelihood of obtaining a non-zero difference
between the two estimates can be tested for statistical signifi-
cance. If this difference is sufficiently close to zero, then the
estimate of summed willingness-to-pay is probably accurate. As
we have seen, this figure is required for the calculation of
noise disturbance prices of tax rates.
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CHAPTER IV
DISCUSSION OF THE QEI QUESTIONNAIRE ON NOISE POLLUTION
A. Introduction
The questionnaire designed by QEI, Incorporated to elicit
responses on costs of urban noise is presented in Figure 4. i .
This questionnaire was developed in response to Task C of the
Statement of Work.
The basic purpose of this QEI Noise Pollution Questionnaire
is to determine a typical urban dweller's willingness-to-pay for
a specific reduction in noise. This questionnaire is basically
an economic type of questionnaire designed to determine people's
willingness-to-pay in specific numbers of dollars for specific
amounts of noise reduction. When a government agency is attempt-
ing to impose standards or regulations to control noise, it is
vital that the agency know approximately how much the public is
willing to pay for noise reduction. Otherwise, regulations may
well be imposed that do not reflect the public's actual desires
on controlling noise pollution, as indicated by their willingness-
to-pay for noise reduction. If the public's willingness-to-pay
for noise control were not known, either regulations would be
imposed that were too lax, implying that the public would eventually
decide that little had been accomplished by imposing the regulations
and that noise was still a problem; or regulations would be imposed
that were too strict, implying that a burden would be imposed upon
the public that it did not wish to bear. In a democratic society
regulations imposed by government agencies should be in accordance
with the actual desires of the people.
1. We wish to acknowledge the assistance of Cambridge Survey
Research in designing and pretesting this questionnaire.
134
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NOISE POLLUTION QUESTIONNAIRE
PREPARED FOR THE EPA BY QEI
OMB Clearance No. 158-S-75002
Hello, I'm taking a public opinion survey under a contract for the
EPA. We're trying to find out how the people of this area feel about
some of the problems facing them. I'd like to ask you a few questions
on a strictly confidential basis.
1. First of all, how would you rate this neighborhood as a place to live?
1. Excellent 2. Good 3. Only fair 4. Poor 5. (Don't know)
2. What would you say is the major problem facing this neighborhood today?
3. Is there anything you particularly like about living here?
4. Is there anything you particularly dislike, or feel should be changed?
5. How long have you lived here? (RESPONSE IN NUMBER OF YEARS)
6. Over that period, do you think the quality of life in the neighborhood
has improved, declined, or stayed about the same?
1. Improved 2. Stayed the same 3. Declined 4. (Don't know)
7. Over the next few years do you think the quality of life in this
neighborhood will improveA decline, or stay about the same?
1. Improve 2. Stay the same 3. Decline 4. (Don't know)
8. About how many hours per day on the average is the radio, or the
television set, or the record player or stereo system used?
hours
9. What time of day would the radio, or the television set, or the
record player typically be used? (MULTIPLE ANSWERS ACCEPTABLE)
1. Morning 2. Afternoon 3. Evening 4, Night 5. (Don't know)
10. Do you own or rent your home?
1. Own 2. Rent
1. Own 2. Rent
11. Do you think you will still be here a year from today or do you
think you might move?
1. Definitely stay (GO TO QUESTION 14)
2. Might move (CONTINUE IN SEQUENCE)
3. Definitely will move (CONTINUE IN SEQUENCE)
4. (Don't know - - GO TO QUESTION 14)
Figure 4.1-1
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QEI NOISE POLLUTION QUESTIONNAIRE
12. (If #2 or #3) What would your major reason be for making a move?
13. Would you move to another part of this neighborhood, to another part of
the Boston metropolitan area or to another state ?
1. Another part of neighborhood
2. Another part of Boston metro area
3. Another state
4. (Don't know)
(INTRODUCTION TO QUESTION # 14 FOLLOWS. )
PLEASE LOOK AT THIS CARD. On it is a ladder with rungs numbered zero
to ten. I'm going to read you a list of common problems. If you feel the
problem very seriously affects you personally in this neighborhood, you
would rate it "10" on the ladder -- "very important". If you are not personally
affected at all by the problem you would rate it "zero". If you feel it is
ic"* somewhat important or somewhat serious, you would put it on one of the
*»1C intermediate rungs of the ladder. Now where would you rate:
*%
<«i£ 14. Robbery and break-ins
>l--ta 15. Street crime and violence
u>n«
,,,^ 16. Air pollution
i»-h 17. Noise
|£M, 18. Dirt and litter
£)£ 19. Traffic and congestion
20. Overall, how noisy would you say your neighborhood is ?
*;^ 1. Very noisy 2. Noisy 3. Not bad 4. Quiet 5. Very quiet
ta. hn
21. Are there any particular sources of noise in this neighborhood that annoy
you?
1. Yes — What?
2. No
22. Which of these statements best describes noise around here?
1. lam frequently bothered and disturbed by noise problems.
2. I sometimes notice noise problems around here.
3. I think noise is not really a problem around here.
4. (Don't know)
23. How about within your house; would you say your house is:
1. Very noisy 2. Noisy 3. Not bad 4. Quiet 5. Very quiet
Figure 4.1-2
136
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QEI NOISE POLLUTION QUESTIONNAIRE
LET'S LOOK AT THIS LADDER CARD. Say that "10" means a particular
thing is a very annoying source of noise around here, while "zero" means
you are never bothered by this source of noise. Now I'm going to read
you a list of possible sources of noise and I'd like you to tell me how you
feel each affects you personally. First of all, how would you rate:
24. Noise from motor vehicles (IF ZERO " GO TO # 30)
25. Noise from large trucks and buses
26. Noise from small trucks
27. Noise from motor.cycles
28. Noise from sports card
29. Noise from regular automobiles or constant traffic
30. Noise from road construction or repairs
31. Noise from building construction or repairs
32, Noise from railroad trains or trolley cars
33. Noise from nearby business establishments
34. Noise from industrial plants or factories
35. Noise from garbage or trash collection
36. Noise from people in the streets or outside
37. Noise from neighbors
38. Noise from household appliances, especially vacuum cleaners, dishwashers,
and lawn mowers
39. On the previous list of appliances, were these primarily your own
appliances or those of your neighbors bothering you?
1. Own 2. Neighbors
40 Taking all the noise problems we've looked at together, where would you
put the overall noise problem in the neighborhood: at "10" -- "very annoying1
at "zero" -- "no problem at all"; or someplace in-between ?
UNLESS RATING IS "ZERO"
41. Again, taking everything together, would you say whatever noise problem
there is here is worse at one particular time of day than others ? When?
1. No time difference 2. Midnight - 6 a.m. 3. 6 a. m. - noon
4. Noon - 6 p.m. 5. 6 p.m. - midnight. 6. (Don't know)
42. Would you say whatever noise problem there is, is worse on weekends or
during the week ?
1. No difference 2. Weekends 3. Weekdays 4. (Don't know)
Figure 4.1-3
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QEI NOISE POLLUTION QUESTIONNAIRE
43. Would you say noise problems are worse in a particular season of the year?
1. Summer 2. Fall 3. Winter 4. Spring 5. {No difference)
6. (Don't know)
44. Would you say noise problems bother you more inside your home or
when you are outside?
1. Inside 2. (No difference) 3. Outside 4. (Don't know)
45. Are there particular rooms in your home where noise is more annoying
than in others ? Which room? Why?
46. Some people find that the kinds of noise we've been talking about
interfere with their lives. Can you think of any ways noise has disrupted
your life recently -- any activity it's forced you to stop, for example ?
I'm going to read you a list of problems that might be caused by noise. Let's
use the ladder scale again. "Ten" means it is a very annoying problem to
you personally while "zero" means it is not a problem at all. If you have
not been bothered at all by the problem in the last year you would rate it "zero".
47. Not being able to enjoy radio, television or records due to other noise
48. Not being able to carry on a conversation or telephone conversation due
to noise
49. Being awakened from sleep by noise
50. Has noise ever caused your home to vibrate? How often?
1. Never 2. Once or twice 3. Sometimes 4. Frequently
51. Do you ever work at home ? (IF YES) Has noise around here ever interfered
with or interrupted such work? (IF YES) What kind of work was that?
1. No
2. yes —no
3. yes — yes
52. In the last year, have you taken any steps to reduce noise around here?
What were they?
53. To avoid noise or get away from it? What were they?
I'm going to read you a list of things that people sometimes do, to deal
with noise. I'd like you to tell me whether or not you've done any of these
in the last year — frequently, sometimes, once or twice, never.
Figure 4.1-4
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QEI NOISE POLLUTION QUESTIONNAIRE
54. Closed windows during warm weather to cut out outside noise
55. Raised your voi.ce or shouted to be heard in a conversation
56. Left home or taken a trip, even briefly, to get away from noise
57. Added soundproofing to your home
58. Considered adding soundproofing to your home
59. Turned up the sound on television or radio or records to cover up noise
60. Turned on television, radio or records specifically to cover up noise
61. Complained to neighbors, landlord or the police about noise
62. Have any of your neighbors complained to you concerning noise you were
making in the past year ? How Often ?
1. Never 2. Sometimes 3. Once or twice 4. Frequently
People have different attitudes toward noise in general -- whether or not it
is a problem and how serious it is compared to other problems.
63. First of all, do you think noise can harm people's physical health?
1. Yes 2. (Not sure) 3. No
64. How about mental or emotional health, can noise harm them?
1. Yes 2. (Not sure) 3. No
65. IF YES TO EITHER # 63 OR #64 Would you say that noise has harmful
effects on physical, emotional or mental health frequently, sometimes or
rarely ?
1. Frequently 2. Sometimes 3. Rarely 4. (Don't know)
66. Do you think your own physical or emotional health has been affected by
noise? How?
1. No
2. Yes -- (Don't know)
3. Yes—
67. Some people say that too much fuss is being make about noise these
days. Let's look at the ladder again and imagine that the top (10)
represents a noisy bustling place and the bottom (zero) represents a calm,
very quiet place. Where on the ladder do you think you personally
would prefer to be ?
68. Where on the ladder do you think the average person would prefer to be?
People have a lot of places where they can spend their money. I'd like
to ask you a few questions about how you might spend your money?
Figure 4.1 - 5
139
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QEI NOISE POLLUTION QUESTIONNAIRE
RENTERS ONLY
69. In which of the following categories is your monthly rent?
1. $100 - $124.99 2. $125 - $149.99
3. $150 - $174.99 4. $175 - $199.99
5. $200 - $224.99 6. $225 - $249.99
7. $250 + Per Month
#
70. Now let's look at this card (SAME AS QUESTION #40) where you
rated the noise level in this neighborhood. Let's say we could
lower the noise level one step, either by the government setting
new standards for noise or by your purchasing some noise re-
ducing device. Everything else about the place and neighborhood
would stay exactly the same, only the noise level would be re-
duced. About how many extra dollars per month do you think you
would be willing to spend for that, if anything?
$ _
71. Now let's say we could lower the noise level three steps. Once
more everything else about the place and neighborhood would stay
exactly the same, only the noise level would be reduced. About
how many extra dollars per month do you think you would be willing
to spend for that?
72. How about if the noise level could be reduced to a level that is
never at all annoying; how much extra money per month would you
be willing to pay for that, if anything?
$
HOMEOWNERS ONLY
73. In which of the following categories is your estimate of the
worth of this home, if you were to sell it today?
1. $10,000 - $14,999 2. $15,000 - $19,999
3. $20,000 - $24,999 4. $25,000 - $29,999
5. $30,000 - $34,999 6. $35,000 - $39,999
7. $40,000 - $44,999 8. $45,000 - $49,999
9. $50,000 +
Figure 4.1-6
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QEI NOISE POLLUTION QUESTIONNAIRE
74. In which of the following categories is your present monthly
property tax payment against your semi-annual property tax bill?
1. $0 - $ 49.99 2. $ 50.00 - $ 99.99
3. $100.00 - $149.99 4. $150.00 - $199.99
5. $200.00 - $249.99 6. $250.00 - $299.99
7. $300.00 - $349.99 8. $350.00 +
#
75. Now let's look at this card (SAME AS QUESTION #40) where you
rated the noise level in the neighborhood. Let's say we could
lower the noise level by one step, either by the government
setting new standards for noise or by your purchasing some
noise reducing device. Everything else about the place and
neighborhood would stay exactly the same; only the noise level
would be reduced. About how many extra dollars per month do
you think you would be willing to pay on your monthly property
tax payment, if anything?
$
76. Now let's say we could lower the noise level three steps. Once
more everything else about the place and neighborhood would stay
exactly the same; only the noise level would be reduced. About
how many extra dollars per month do you think you would be willing
to pay on your monthly property tax payments, if anything?
$
77. How about if the noise level could be reduced to a level that is
never at all annoying; how much money per month would you be willing
to pay for that on your monthly property tax payment, if anything?
$
78. How concerned are you about the current economic situation?
1. Very concerned 2. Somewhat concerned
3. Slightly concerned 4. Not at all concerned
79. How much would your concern with the present economic situation
affect your willingness-to-pay for noise reduction?
1. Very much 2. Somewhat
3. Not too much 4. Not at all
Figure 4.1-7
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QEI NOISE POLLUTION QUESTIONNAIRE
To complete the analysis for this survey, we would like some addi-
tional information about your background.
80. What is your age? (record years)
81. What was the last grade you completed in school?
1. Some grade school (1-8) 2. Some high school (9-11)
3. Graduated high school 4. Technical or vocational school
5. Some college 6. Graduated college
7. Post-college, graduate or professional study
82. Are you the principal wage-earner in this household or is
someone else? (IF SOMEONE ELSE) What was the last
grade (he/she) completed in school?
1. Some grade school (1-8) 2. Some high school (9-11)
3. Graduated high school 4. Technical or vocational school
5. Some college 6. Graduated college
7. Post-college, graduate or professional study
83. (CHOOSING FROM THIS LAST QUESTION) What is (your/the principal
wage-earner's) Occupation?
1. (Employed full-time) 2. (Employed part-time)
3. (In temporary employment) 4. (Self-employed)
5. (Unemployed) 6. (retired)
7. (A Student) 8. (On Welfare)
9. (Other - Specify
84. (IF 1,2,3,4 TO ABOVE) What kind of organization does (he/she)
work for? What kind of service or product does it produce?
85. (IF 1,2,3,4 TO #83) What kind of job does (he/she) have?
86. How many rooms, not including bathrooms, are there in this house
or apartment?
87. How many children under 18 years of age and living at home are
there in your family?
Figure 4,1-8
142
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QEI NOISE POLLUTION QUESTIONNAIRE
88. Do you have air-conditioning?
l- Yes 2. No 3. (Partial - in some rooms)
90.
89. Do you have double or thermo-pane windows, or do you just
have a single pane of glass?
1. Double 2. (Not sure) 3. Single
In which of the following categories is your total family income?
4. $15-$19,999
1. $0-$4,999 2. $5-$9,999
5. $20-$24,999 6. $25,000+
3. $10-$14,999
7. (Refused)
#
THANK YOU!
Address
Phone
Interviewer I.D.
91. Sex
1. Male
92. Race
1. White
93.
2. Female
2. Black
3. Other
Type of home:
1. Detached - single family
2. Duplex
3. Single family - row or attached
4. Apartment - less than 4 floors or 40 units
5. Apartment - more than 4 floors or 40 units
6. Mobile home
7. (Other - specify
94. (IF 4 or 5 TO ABOVE) Floor on which respondent lives
~&5~. d B(A> Heading " " " '
Analytic data: (Not interviewer-available)
96. Distance from Nearest Point of Airport or Flight Path
Figure 4.1 - 9
143
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QEI NOISE POLLUTION QUESTIONNAIRE
97. Distance from Nearest Point of Super Highway (number of lanes
on the nearest super highway should be noted if possible, number
of heavy trucks per minute moving along the highway^ also)
98. Distance from Nearest Point of Rapid Transit Line or Railroad
99. Distance from Nearest Construction project (possibly) (Size of
construction project and number of air compressors, generators,
etc. at the construction site should be noted)
100. One of the following: Census Tract population density/ or /
people per room ratio/ or /average housing value/ or /some
combination of objective census facts.
Figure 4.1 - 10
144
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QEI NOISE POLLUTION QUESTIONNAIRE
NOISE POLLUTION LADDER CARD
10 ---------------------------------- Very Annoying
9 ----------------------------------
g __________________________________
7 ---------------------------------- Rather Annoying
6 ----------------------------------
A __________________________________
3 ---------------------------------- Somewhat Annoying
o __________________________________
1 ---------------------------------- A Little Annoying
0 ---------------------------------- Not At All Annoying
No Problem At All
Figure 4.1 - 11
145
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It is, of course, assumed that the annoyance caused people by
excessive noise and thus their willingness-to-pay for its reduction
are highly correlated with some observable physical measurement of
noise intensity. If this assumption is proven false, there will be
no way of imposing noise standards so that the desires of the public
are fulfilled. Any noise control standards or regulations that are
imposed must, of course, be stated in terms of some directly measurable
quantity such as a physical measurement of noise intensity. The as-
sumption that there is a high correlation between annoyance caused by
noise and some physical measurement of noise intensity is, of course,
basic to the justification for taking such a survey as this. This
assumption does, however, seem to be justified by certain other re-
search such as that reported in the Griffiths and Langdon paper (7)
and the Foreman, Emmerson, and Dickinson paper (5).
However, the questions on an individual's willingness-to-pay for
noise reduction cannot be asked immediately and must be led into
gradually by obtaining people's imprecise general views on how serious
noise pollution really is. In addition, this questionnaire includes
questions on various secondary, but still important, aspects of noise
pollution. One of these secondary aspects is the sources of noise
believed to be the most important contributors to the entire noise
pollution problem. It is necessary to know the most important sources
of noise in order to set standards and regulations for noise in
an efficient and effective manner. It is obviously desirable to be
able to concentrate on the most important sources of noise pollu-
146
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tion when attempting to impose standards for noise control.
Questions are also included in the survey on the particular
activities of the respondent that noise has often interfered with.
It is important to know which activities have been interfered
with by noise in order to determine people's general attitudes
toward noise pollution in relation to the activities that they
deem most desirable. Naturally, questions must be included in
the survey on the socio-economic status of the respondent in
order to test various hypotheses about the relative sensitivity
of different classes of people to noise.
This questionnaire should also include questions which will
indicate if the respondents are answering the questionnaire under
any constraints limiting their willingness-to-pay for noise
reduction. One constraint on people's willingness-to-pay for
noise reduction is certainly lack of available funds; so there-
fore questions are asked about the respondents total family
income. A second constraint would appear to be how much the
respondents have already spent on noise averting devices. If
they have already installed an air conditioner or double pane
glass in their windows, they will certainly be much less willing
to spend more for noise reduction. This is in part due to the
fact that by purchasing and using these noise-reducing devices,
they have certainly reduced their problems with noise pollution.
This is also due in part to the fact that purchases of noise-
reducing devices have depleted their available funds. Thus,
the respondents are asked if they have an air conditioner or
147
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double pane glass in their windows. A third constraint on the
respondents' willingness-to-pay for noise reduction might be the
principal source of the noise. If some of the respondents believe
that the source of noise that is causing them the most annoyance is
basically uncontrollable, they would be less willing to pay for noise
control. (Such an uncontrollable noise source might be children.)
Once these constraints on the respondents' willingness-to-pay are
recognized, they can be taken into account in the analysis.
The most important group of questions in the survey, those re-
lating to people's willingness-to-pay for a specific reduction in
total noise - were devised by QEI personnel and consultants during
the course of this contract. The other questions in our survey were
inspired in part by questions asked in other surveys on noise pollution.
The following sources for surveys were particularly important in pro-
viding inspiration in designing our secondary questions: l)Bolt, Beranek,
and Newman, "The E.P.A. 24 Site Survey Questionnaire", Spring, 1974;
2) Bolt, Beranek, and Newman, Feasibility of a Novel Technique for As-
sessing Noise-Induced Annoyances, September, 1973; and 3) Wyle Labora-
tories, A Program for the Measurement of Environmental Noise in the
Community and Its Associated Human Response, Volume II, December, 1973.
The following pages present a discussion of the various groups of
questions in the QEI Noise Pollution Questionnaire, taken in the se-
quence in which they appear in the questionnaire. This discussion
will elucidate the reasons for including these particular questions in
the questionnaire, and will indicate the relevance of each question to
the general topic of noise pollution. The discussion will also contain
indications of the uses to which the answers to these questions will be
put in any subsequent analysis of the responses to the survey.
148
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B. General Questions on Attitudes Toward Noise
Questions 1-4 are general questions about the environment in which
the respondent lives. Hopefully these questions will elicit some
general indication from the respondent as to the seriousness of noise
pollution in his neighborhood. It is believed that many of the res-
pondents who are very annoyed by noise pollution will mention noise as
a problem in response to these questions. These questions should give
an indication of the importance of noise to the respondents relative
to other environmental problems.
Question 5 attempts to determine how long the respondent has lived
in that particular neighborhood. There is some evidence which indicates
that people who have lived in a neighborhood for a substantial period
of time are more annoyed by noise of a certain intensity and frequency
of occurrence than are people who have only recently moved to the
neighborhood. For instance, the Rylander, Sorenson, and Kajland survey
indicated that the percentage of people who had lived in a neighborhood
for more than ten years and who were "very annoyed" at noise of a cer-
tain intensity was four times the percentage of people who had moved
to the neighborhood within the last year and who were "very annoyed'1.
(See Ref. 8, pp. 432-433). This seeming increase in annoyance at noise
pollution with increasing length of stay in a neighborhood appears to
be due to a person's increasing commitment to a neighborhood and in-
creasing unwillingness to leave as his length of stay in the neighborhood
grows. Thus, one of the reasons for asking this question is to deter-
mine how much a person's willingness-to-pay for a specific reduction
in noise pollution is affected by the length of his stay in a particular
neighborhood. Also, it is usually believed that the rate at which people
149
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move into and out of a neighborhood is a good indicator of the stability
and continuity of the neighborhood. An approximation to the rate of
housing turnover for a particular neighborhood could be calculated
by taking the average of all the responses to this question for a
neighborhood. Thus, the responses to this question might be mani-
pulated to yield a basic socio-economic indicator (to be used in the
following analysis) for some of the neighborhoods surveyed, anyway.
Questions 6-7 are general questions asked to determine how people
think their entire environment is changing over time. Hopefully these
questions will indicate the respondent's basic view of their future
environment. Question 7 should determine whether the respondents
are basically optimistic or pessimistic about their future environment
and question 6 should indicate a part of the basis for their optimism
or pessimism, respectively.
Questions 8-9 are asked to determine how often most of the noise
pollution around a person is being blanked out, either because of a
conscious or unconscious desire to eliminate the unwanted noise or
because of a conscious desire to listen to some sort of entertainment.
It was believed that it was unimportant to distinguish among sound
produced by radio, television, or record player for the purposes of
this survey, since we only wish to learn how often people regularly
blank out noise.
Question 10 is a request for a basic piece of information about the
respondent (does he own his home or not) which will determine the basic
form in which the questions on his willingness-to-pay for noise reduction
will be asked. It is also of interest to determine if ownership of
one's home affects one's willingness-to-pay for noise reduction.
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Questions 11-13 constitute another method of determining the res-
pondent's general level of satisfaction with his total environment.
Thus, the answers to these questions should provide something of a
cross-check on the answers given to questions 1-4. The answers to
these questions for a group of respondents from the same neighborhood
will also give an indication of the basic stability of the neighborhood,
which is an important socio-economic variable, as was mentioned above.
Questions 14-19 will force the respondents to compare the annoyance
caused them by noise with the annoyance caused by other environmental
menaces or nuisances. These questions should elicit a specific in-
dication as to approximately how important the respondents consider
noise in relation to other environmental hazards. Up to this point
no questions have been asked specifically about noise. The basic
purpose of avoiding questions specifically on noise initially is to
induce the respondents to give an unbiased estimate of how annoying
noise really is to them. Those respondents who believe that noise is
a very serious problem and are very much annoyed by it are given the
opportunity to bring up noise by themselves, thereby indicating their
great concern over this type of pollution. It was believed that in-
dicating that noise was our principal concern would bias people's
initial responses on what they considered to be the most annoying
environmental problems in their neighborhoods. It was hoped that
people would respond with their true normal reactions to noise if the
questions were asked in this manner, rather than trying to please the
interviewer or discourage and get rid of him. It should be made clear
that this manner of asking questions does not involve deceiving the
respondents or persuading them to say things that they do not really mean.
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In questions 20-23 the respondents are finally asked specifically
about their reactions to noise, following the gradual lead-in to
questions on noise. These four questions are general questions con-
cerning the annoyance caused the respondents by noise. It should be
noted that these four questions contain a certain amount of cross-
checking within themselves. Also, the responses to these questions
can be cross-checked against the responses to earlier questions, par-
ticularly questions 1-4 and 17.
Questions 24-39 attempt to determine the relative importance of
the various sources of noise to the respondent. The answers to these
questions should indicate which sources of noise pollution it is most
desirable to regulate and control, assuming, of course, that the sources
of noise pollution which should be controlled are those which cause
people the most annoyance. The Foreman, Emmerson, and Dickinson sur-
vey (5) conducted in London and Woodstock, Ontario, indicated that motor-
cycles were the most bothersome source of noise, and it would be in-
teresting to confirm or dispute this finding. The respondents are
aksed only one question about noise sources, such as pets, children,
and adult neighbors (talking, fighting, having noisy parties) since
laws regulating such noise sources would be very difficult to have
adopted and would be virtually impossible to enforce. Specific instances
of noise from such sources might be (and sometimes are) controlled,
but any such control would have to proceed on a case-by-case basis.
Thus, since information obtained about such noise sources could not be
readily used to set standards or regulations, it seemed pointless to
ask questions about these sources. Questions are not asked about noise
sources such as aircraft and airports since these sources were covered
by similar contracts.
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Questions 40-41 are general questions on the annoyance caused by
all sources of noise taken together. Since these questions relate to
the level of annoyance caused by noise from all sources, they con-
stitute a cross-check on other questions on this issue, particularly
questions 20-23.
Questions 42-43 bear on the problem of determining the seasonal
period or duration of sampling as mentioned in Task E of the Statement
of Work. Determining when such a noise pollution survey as this
should be taken and determining if return visits to the original res-
pondents at a later time are desirable is a difficult problem;.due to
the variations in both overall noise level and the vulnerability of
people to noise over the course of a year. (It is assumed that people's
more recent experiences impress them more than experiences that occurred
a long while ago.) Other than the problems caused in sampling due to
the variations in the effects of noise over time, these variations
raise considerable problems in determining how to combine samples of
public reactions to noise taken at different times or how to take ac-
count of these variations when dealing with a sample taken at one par-
ticular time.
Questions 44-45 pertain to the spatial distribution of noise in
and around the respondent's home. Question 44 should also provide
a cross-check on question 43.
Questions 46-51 attempt to ascertain the activities of the res-
pondent that noise interferes with, and the seriousness or extent of
such interference. Initially, the respondents are asked to name
activities that noise has often interfered with. Then, a specific
activity is mentioned and the respondent is asked if noise has inter-
153
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fered when he has been engaged in that particular activity, and how
frequent such interference with this activity has been. This method
of asking the respondent to name activities that noise has interfered
with and then asking him particularly about various activities noise
could interfere with should expose more of the respondent's actual
feelings on this topic. The response to question 46 will provide some-
thing of a cross-check on the responses to questions 47-51. Rest and
relaxation (inside or outside) are not included in the list of specific
activities that the respondent is questioned about since it is dubious
that the effect of noise on them is much different from its effect
on many other activities such as cleaniBg the house, preparing meals,
or weeding the garden. It seemed unnatural to single out rest and
relaxation from among a group of activities on which noise would have
yery similar effects. Conversation (and the other activities on which
the respondent is specifically questioned) are very different in that
transmission of sound is involved. (The basic list of activities that
noise might interfere with was derived from the Wyle Laboratories sur-
vey O) )•
Questions 52-62 pertain to things the respondents might have done
recently to reduce noise around the home or to avoid it. Once more
the technique is used of initially asking the respondent to name actions
he has performed to reduce noise around his home or avoid it; then a
list of actions that are often performed to reduce noise or avoid it
is read and the respondent is asked how often he has done these specific
things. It is hoped that this method might best elicit the respondent's
true response to noise. Questions 52-53 should provide something of a
cross-check on questions 54-62.
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Questions 63-66 pertain to the respondent's attitude toward the
effects of noise on people's physical, mental and emotional health.
While the effects of noise on people's physical, mental and emotional
health are only one aspect or part of the total problem caused by
noise pollution, they are certainly a very important part. People's
annoyance with noise pollution is certainly in part an expression of,
or a reflection offttheir beliefs about the effects of noise on their
health and on that of other people. The survey taken by Foreman,
Emmerson and Dickinson (5) found that some 30% of the respondents believed
that excessive noise had some deleterious effect on people's health.
It should be noted that this survey was taken in a relatively small
urban area - London and Woodstock, Ontario - so that it might well be
that in a large urban area, a much larger percentage of people would
be concerned about the effects of noise on health.
Questions 67-68 pertain once more to the respondent's basic at-
titudes toward noise pollution. As such, these questions constitute
a further cross-check on the responses given to questions 20-23.
C. Questions on Willingneas-to-Pay for Noise Reduction
Questions 69-77 constitute the principal focus of this question-
naire. These questions attempt to ascertain people's willingness-to-
pay for specific reductions in the perceived total noise level. These
questions are, of course, based on the assumption that the respondents
would engage in no more or no less or no other noise-averting activities
than they are presently engaged in, no matter how much the noise level
is reduced. (We know approximately how much noise-reducing activity
the respondents are presently engaged in from their answers to pre-
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vious questions on this questionnaire, particularly questions 54-61.)
This is, of course, a rather strong assumption, but seems to be virtually
necessary to avoid a long explanation to the respondents about noise-
averting actions. These questions are divided into two sub-groups,
questions 69-72 being designed for those respondents who rent their
homes, and questions 73-77 being designed for those who own their homes.
This division of respondents into renters and home-owners appeared
necessary due to the differing methods of paying rent and paying for
home ownership. It also seemed possible that people who own their
"homes might have a different attitude toward the noise in their neighbor-
hood than those who rent. Both groups of questions, questions 69-72
and questions 73-77 are organized in the same manner and consist of
questions that are very similar.
First, the respondents, both renters and homeowners.,are asked for
an estimate of the amount they pay each month for the use of their
home or apartment. (Categories of rent payments and monthly tax pay-
ments for owned homes are presented to the respondents since it was
believed that they would be more responsive to indicating a range
than they would be to giving a precise number of dollars.) Then the
respondents are asked how much they would be willing to pay for a
reduction of one unit in the annoyance caused them by noise. These
questions attempt to determine the respondent's willingness-to-pay for
unit reduction in the noise level. Then both groups of respondents are
asked how much they would be willing to pay for a reduction of three
units in the annoyance caused them by noise. It was believed that there
might be certain situations, such as where the noise level was very
high, in which a reduction in the noise level by only one unit would
make very little difference to the respondent. A unit reduction in
noise level might make no appreciable difference to some respondents
156
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in certain neighborhoods. Thus, it was decided to ask about a three
unit reduction in noise level as well as a one unit reduction, in
part, to determine if such situations were prevalent, and, in part,
to test the assumption of linearity for people's willingness-to-pay
for noise reduction. Lastly, the respondents are asked how much they
would be willing to pay for a reduction in noise level to a point
where it is never at all annoying. (It is assumed here that annoyance
caused by noise and some physical measurement of noise intensity are
highly correlated. This assumption seems to be justified by certain
other research such as that reported in the Griffiths and Langdon
paper (7) or the Foreman, Emmerson, and Dickinson paper (5). Noise
regulations must, of course, be stated in terms of some physical
measurement of noise.) It should be noted that the respondents will
not be forced to say that they would pay anything at all for any re-
duction in noise pollution, no matter how large. Paying nothing for
a reduction in noise pollution is presented to the respondents as an
option.
Questions 78-79 represent an attempt to determine how the current
economic situation is affecting the respondents' answers to the econ-
omically-oriented questions in the survey. It seems very likely that
the current recession is having an effect on people's willingness-to-pay
for a reduction in the noise level. (Three possible effects on people's
willingness-to-pay to reduce the noise level seem possible: 1. the
effect caused by the fact that the cost of reducing noise is increasing
faster than some people's salaries; 2. the effect caused by fear of
future unemployment; and 3. the effect caused by the fact that
available housing is becoming hard to find and thus people are pre-
vented from moving to escape excessive noise.) When economic con-
ditions change, the answers received to certain questions on
157
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this survey may well change for some respondents . It
would be nice to include some indicator of the current economic
situation in the analysis of responses to certain questions in this
questionnaire (or in any economically-oriented questionnaire). How-
ever, substantial research will have to be done to find an appropriate
means to insert the answers to questions such as these into an analysis
of responses to the willingness-to-pay questions in this questionnaire.
Questions on Respondent Characteristics
Questions 80-86 and 90 are included in this survey in an attempt
to determine the approximate socio-economic level of each respondent.
The socio-economic level of a respondent is determined in part by
his income level but also in part by his occupation, amount of education,
etc. It is suspected that a person's socio-economic level may well
influence his willingness-to-pay for a reduction in the noise pollution
level. Persons at higher socio-economic levels might well be more
conscious of noise and thus willing to pay larger amounts for its re-
duction. The answers to these questions might well be used in some
sort of analysis, such as a regression analysis, of the answers to the
willingness-to-pay for noise reduction questions.
The answer to question 87 will serve to establish in part the ap-
proximate ambient noise level in the home, or that level of noise which
is usually present in the respondent's home. The answer to question
88 serves to establish the vulnerability of the respondent to noise
during the summer, or to indicate a cause for the respondent's annoy-
ance with noise pollution during the summer. The answer to question
8?9 serves to establish in part the vulnerability of the respondent to
158
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noise during the fall, winter and spring, and probably to a lesser
degree, during the summer. The response to question 89 will also
serve to suggest just how serious the noise problem in the respondent's
area really is.
E. General Information on the Respondent
The respondent is only asked to answer questions 1-90. Numbers
91-100 on the questionnaire correspond to information desired about
the respondent or his environment which the interviewer is supposed
to fill in for each respondent. The respondent should not be asked
for the information corresponding to numbers 91-100. The interviewer
or his superior should fill in this information for each respondent
following the interview.
Numbers 91-93 and 100 will provide basic socio-economic information
on the respondent that could be used in an analysis of the respondent's
answers to the questions on his willingness-to-pay for noise reduction.
Number 94, the floor on which the respondent resides, if he lives
in an apartment house, is very important in determining his vulner-
ability to ground-level sources of noise pollution, such as vehicular
traffic and much construction work. If the respondent lives on one
of the upper floors of a high-rise apartment building, he will obviously
be very slightly affected by ground-level sources of noise.
Numbers 95-99 request pieces of information which determine to
some extent the noise level v/hich is actually present in and typical
of the respondent's home. Thus, this information will give us some
indication of the actual noise level that the respondent is reacting
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to. This will be used to determine the respondent's general sensitivity
to noise and could be used to identify and possibly separate out
people who were abnormally sensitive or abnormally insensitive to noise.
The analysis should obviously concentrate on the reactions of normal
individuals to noise. The information given here, when organized by
neighborhoods, will indicate the most important noise sources in the
neighborhoods.
160
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REFERENCES
1. Bolt, Beranek, and Newman, Incorporated, "E.P.A. 24 Site Survey
Questionnaire", Spring, 1974.
2. Bolt, Beranek, and Newman, Incorporated, Feasibility of a Novel
Technique for Assessing Noise-Induced Annoyance, Office of
Noise Abatement, September 1973. NTIS #: PB-225 334.
3. Borsky, Paul N., "The Use of Social Surveys for Measuring Com-
munity Responses to Noise Environments", in Chalupnik,
James D., ed., Transportation Noises, University of Washington,
Seattle, Washington, 1971.
4. Bregman, Howard L., Development of a Noise Annoyance Sensitivity
Scale, North Carolina State University, Raleigh, North Carolina,
February 1972. NTIS #: N72-16005.
5. Foreman, J.E.K., M.A. Emmerson, and S.M. Dickinson, "Noise Level/
Attitudinal Surveys of London and Woodstock, Ontario", Sound
and Vibration, December 1974.
6. Franken, Peter A., "Aircraft Noise and Airport Neighbors: A
Study of Logan International Airport", Bolt, Beranek, and
Newman, Incorporated, March 1970.
7. Griffiths, I.D. and F.J. Langdon, "Subjective Response to Road
Traffic Noise", Journal of Sound and Vibration, 8:1, 1968.
8. Rylander, R. , S. Sorensen, and A. Kajland, "Annoyance Reactions
from Aircraft Noise Exposure", Journal of Sound and Vibration,
24:4, 1972.
9. Wyle Laboratories, A Program for the Measurement of Environmental
Noise in the Community and its Associated Human Response,
Volume II, A Plan for a National Program. Department of Trans-
portation, December 1973. NTIS #: PB-228 564.
161
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CHAPTER V
DESCRIPTION OF THE PRETESTING OF THE
QEI NOISE POLLUTION QUESTIONNAIRE
AND DISCUSSION OF RESULTS
A. Selection of the Sample for the Pretest
The selection of the sample to be tested with the QEI Noise
Pollution Questionnaire was performed in accordance with the following
general principles. First, it was decided to pretest the instrument
on geographical clusters of respondents. Respondents were chosen in
such a manner that each respondent lived fairly near nine or ten
other respondents. The basic reason for selecting geographical clusters
of respondents was to obtain some indication of individual differences
among people reacting to the same stimulus or the same level of noise
pollution. The variability among individuals reacting to the same
noise level seemed an important area to investigate early in the
analysis, since if variability among individuals were very high, it
might imply that any standards or regulations for noise that could be
imposed would be either much too lax or much too strict for most of
the population.
Second, it was decided to select the sample to be surveyed largely
from areas with a high incidence of traffic noise. The sample was
chosen in large part from areas near major highways or important main
streets. We wanted to insure a positive response to the questions on
this survey, rather than obtaining responses from people who were pro-
bably not seriously bothered by noise pollution. This latter group
will, of course, be well represented in the sample that will be asked
to respond to the final version of the questionnaire; but in performing
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the pretest we wanted a sample that would allow us to test all the
questions in the survey. In performing the pretest we wanted a sample
of respondents whose answers would test the upper limits or extremes
of the questionnaire.
Third, the sample to be pretested must be chosen from areas that
are not affected by noise from aircraft or airports. Noise pollution
produced by aircraft or airports will be examined in surveys conducted
under similar contracts. Thus, to avoid overlapping with such efforts,
areas in which aircraft noise is an important contributor to the total
level of noise pollution will not be included among the areas to be
surveyed.
For the pretest, it was decided to use a sample of at least 60.
It was believed that the answers to a survey of this size would re-
flect the income variability of the entire Boston SMSA fairly ac-
curately, since the income variable has been restricted on this
questionnaire to six mutually-exclusive categories. The variability
of income rather than that of some other variable was chosen to
determine the sample size for this pretest since income was believed
to be the most important determinant of variation in response for this
study. The sample size was determined from standard formulas assuming
a normal distribution in income.
B. Selected Results of the Pretest
Sixty (60) persons, ten from each of six neighborhoods in the
Boston metropolitan area were pretested with the QEI Noise Pollution
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Questionnaire. This pretesting indicated that the QEI Noise Pollution
Questionnaire does not require any major changes or modifications. All
of the questions appeared to be readily comprehensible by the sample
of persons pretested. The interviewers indicated that they had no
difficulty obtaining reasonable responses from the individuals surveyed
to any of the questions included in this questionnaire. However, it
does appear that minor modifications might be desirable for three of
the included questions.
The distribution of total family income for the persons pretested
appears to be approximately normal, with the largest deviation from
a normal distribution occurring in the right- and left-hand tails.
However, a fairly large percentage of the respondents, nearly 22%,
either refused to indicate the category in which their income lay or
said that they did not know what their family income was. This implies
that the size of the sample used for the actual test should be some
25-30% larger than calculated, to compensate for this large number of
refusals. (Hopefully, not much bias will be introduced by this procedure)
Figure 5.1 shows the distribution of total family incomes by categories
for the sample pretested. Calculations on this distribution gave a
mean of approximately 3.5 and a variance of approximately 1.8.
The distribution for monthly property tax payments for owned
homes also seems to be approximately normal, with the largest deviation
from normality appearing to be a small skewing toward the lower tax
payments. Figure 5.2 shows the distribution of monthly property tax
payments for owned homes by categories for the sample pretested.
Calculations on this distribution gave a mean of approximately 3.9
and a variance of approximately 1.1. However, it should be noted
164
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$0 -
$4,999
$5 -
$9,999
15
$10 -
14
$15 -
$14,999 ! $19,999
$20 -
$24,999
$25,000
+
FIGURE 5.1
Distribution of Total Family Incomes for the Pretest Sample
165
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$0 -
$49.99
$50.00
$99.99
$100.00
$149.99
$150.00
$199.99
$200.00
$249,99
$250,00
$299.99
FIGURE 5.2
Distribution of Monthly Property Tax Payments
on Owned Homes for the Pretest Sample
166
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that the sample on which these calculations are based is a little
small, twenty; so that computations done on this sample certainly
give rather gross approximations.
The distribution for rent is very unusual in that it is totally
dissimilar from a normal distribution. The rent distribution appears
to be a bimodal distribution with the two modes falling in the lowest
and in the highest categories for rent. This distribution seems to
be quite similar to one of the forms of the beta distribution. How-
ever, the distribution is based on a rather small sample, thirty-four;
so that it is dangerous to draw conclusions on the basis of this dis-
tribution. (The peculiar form of the distribution for rents is pro-
bably due to the fact that for the pretest respondents were selected
so that each belonged to a geographical cluster of respondents. This
method of selection combined with the small number of clusters, six,
has undoubtedly led to a non-random selection of housing types, due to
the tendency of similar housing types to cluster together.) Figure
5.3 shows the distribution of rents by categories for the sample pre-
tested. It can be concluded from this distribution that the actual
survey should include a fairly large number of renters, so that any
peculiarities in the distribution of rents due to the small size of
the sample will be overwhelmed and eliminated.
Nearly 40% of the sample pretested had some sort of air con-
ditioners, either partial or throughout the house. This implies that
the total variation in annoyance with noise over the seasons will be
substantially smaller than if air conditioners were not so popular.
Those who have air conditioners will be far less annoyed by noise
during the summer than those who don't. Around 53% of the sample have
double-pane glass in their windows, or mentioned that they had storm
167
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9
$100.00
$124.99
$125.00
$149.99
$150.000
$174.99
$175.00
$199.99
$200.00
$224.99
13
$225.00
$249.99
$250
FIGURE 5.3
Distribution of Monthly Rent Payments for the Pretest Sample
168
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windows in response to this question. Storm windows could be most
effective in reducing annoyance due to noise, since storm windows
can be left up on the noisiest sides of the house during the summer.
70% of the sample had either air conditioning or double-pane windows
(including storm windows) or both in their homes. This implies that
a substantial part of the populace will be less willing to pay for
noise reducing devices, since they have already spent money for such
devices. The part of the population that has air conditioning and/or
double-pane windows will not only be less annoyed by noise pollution
than those who do not have such devices, but will be less willing to
spend money for noise reduction, having already spent funds for this
purpose.
Certain of the other results from the pretest also appear to
be of interest, though they will not have any affect on the method
of selecting the sample of persons to be interviewed for the actual
test. It should be remembered, however, that these pretest results
were derived from a rather small sample of respondents. Also, the
distribution of rents seems to indicate a bias in the selection of
renters away from those who pay moderate rents. Thus, one should be
most careful in drawing any firm specific conclusions on the basis of
the results presented below. Nevertheless, we believe that these pre-
test results do indicate certain general tendencies or trends in the
data. We believe that certain very general conclusions may be drawn
from the results presented, and that these results do indicate certain
basic trends in the data.
First, the pretest results indicate that people in this area
believe noise to be one of the most important environmental problems.
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The people interviewed said that they considered noise to be the en-
vironmental problem that affects them most seriously, as compared to
such other environmental problems as traffic and congestion, dirt and
litter, air pollution, robbery and break-ins, and street crime and
violence. (It should, of course, be remembered that the respondents
chosen for the pretest were often selected to come from areas where
there was believed to be traffic noise problems, such as areas near
major highways.) The precise numerical ratings of environmental
problems will be given below for the pretest sample. However, it
seemed appropriate to divide the pretest respondents into renters and
home owners, because it was believed that renters might be more
critical with respect to environmental problems that home owners,
since renters would seem to be less responsible and less blameable
than would home owners. A statistical test on the difference between
the renters' mean rating of noise and the home owners' mean rating of
noise indicated that this difference was indeed significant.
The mean rating of the seriousness of noise by the renters
compared to their mean ratings of the seriousness of other environ-
mental problems is presented in Figure 5.4; while the home owners'
mean rating of the seriousness of noise as compared to their mean
ratings of other environmental problems is presented in Figure 5.5,
The mean rating of the seriousness of noise for both renters and
owners combined as compared to their mean ratings of other environment-
al problems is presented in Figure 5.6. The distributions of the
noise ratings for renters, owners, and renters and owners combined
are presented in Figures 5.7, 5.8, and 5.9 respectively. These dis-
tributions indicate something of a tendency of these seriousness of
170
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Environmental Problems
Noise
Traffic and Congestion
Dirt and Litter
Air Pollution
Robbery and Break-ins
Street Crime and Violence
Figure 5.4
Mean Value of the Renters'Ratings of the Seriousness of Various
Environmental Problems from the Pretest
Environmental Problems
Mean
6.
5.
5.
5.
4.
3.
0
4
S
3
3
2 3
1
1 ; 3
1 3
6 : 3
.D.
.2
.3
.1
1
.5
.6
.5
Noise
Traffic and Congestion
Dirt and Litter
Air Pollution
Robbery and Break-ins
Street Crime and Violence
Mean
3
2
3
2
2
0
.6
.9
.4
.4
.1
.5
S
3
3
3
2
3
1
.D.
.5
.4
.8
.5
.1
.1
Figure 5.5
Mean Values of the Home Owners' Ratings of the Seriousness of
Various Environmental Problems4 from the Pretest
171
-------
Environmental Problems
Noise
Traffic and Congestion
Dirt and Litter
Air Pollution
Robbery and Break-ins
Street Crime and Violence
Figure 5.6
Mean Values of the Combined Renters' and Home Owners' Ratings of the
Seriousness of Various Environmental Problems^ from the Pretest
Mean
5.0
4.4
4.4
4.0
3.3
2.3
S.D.
3.5
3.5
3.5
3.3
3.5
3.2
7-
6-
5'
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i
•
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i
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Figure 5.7
8
10
Distribution of Renters'Noise Ratings (in Comparison to Other
Environmental Problems) from the Pretest
172
-------
7-
6'
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Figure 5.
8
Distribution of Home Owners' Noise Ratings (in Comparison to Other
Environmental Problems) from the Pretest
11-
10-
9-
8-
7-
6-
5-
4«
3'
2'
1«
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. 4
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t
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Figure 5.9
Distribution of Combined Renters' and Home Owners' Noise Ratings
(in Comparison to Other Environmental Problems) from the Pretest
173
-------
noise ratings to cluster around the highest and the lowest ratings.
The ratings assigned by the respondents to the overall noise
levels in their neighborhoods (from Question 40) are also rather
interesting. Once more it seems appropriate to separate the respon-
dents into renters and home owners, since renters may well be more
critical of problems for which they are blameless. The mean rating
on the seriousness of overall noise is 4.6 for renters and 2.5 for
home owners. This does seem to indicate that home owners regard noise
as a less serious problem than renters possibly because home owners
usually live in more expensive, less densely populated and thus less
noisy areas than renters and possibly because owners are better able
financially and practically to take steps to reduce noise. The initial
entries in Figures 5.4 and 5.5 are also the mean rankings assigned by
the respondents to the annoyance caused them by the overall noise
level. These mean rankings for disturbance caused by noise are 6.0
for renters and 3.6 for home owners. The differences between the
renters' two mean rankings for annoyance caused by noise, 6.0 and 4.6,
and between the home owners' two mean rankings for annoyance due to
noise, 3.6 and 2.5, are sufficiently large to cause concern. It is
disturbing that the responses to two different ways of asking the same
basic question should be answers that vary so widely. Part of the ex-
planation for these large differences in answers may be due to the
smallness of the samples; part may also be due to flaws in the wording
of the questions or to errors in administering the questionnaire.
Nevertheless, it is certainly possible that these two different methods
of asking the same basic question may produce different reactions in
some respondents. The distributions of noise ratings for renters and
home owners are presented in Figure 5.10 and Figure 5.11. These dis-
174
-------
8
7
6-
5-
4'
3
2
1
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Figure 5.10
Distribution of Renters' Noise Ratings from the Pretest
9-
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9
10
Figure 5 •11
Distribution of Home Owners'Noise Ratings from the Pretest
175
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tributions differ very widely in their basic shape. Figures 5.10
and 5.11, of course, represent responses to basically the same
question as Figures 5.7 and 5.8.
Another interesting difference between the reactions of renters
and home owners to noise is shown by the relative importance assigned
by each group to the various sources of noise. Figure 5.12 shows the
mean rankings of five different noise sources by renters and home
owners. These figures show that while renters consider large trucks
to be the most important source of irritating noise, home owners con-
sider regular automobile traffic to be the most annoying source of
noise. The reason for this is probably the presence of more large
trucks in the areas principally inhabited by renters, areas near large
industrial and commercial establishments in many cases.
The pretest results giving personal willingness-to-pay for noise
reduction are also rather interesting. Once more it seems desirable
to separate the pretest sample into renters and home owners. One
good reason for this separation is that home owners have somewhat
higher incomes than renters. Since home owners have more money avail-
able to them than renters, home owners might well have either spent
more or be willing to spend more for noise reduction than renters.
Also, home owners usually live in less densely populated and thus less
noisy areas than renters.
The pretest indicated that renters would be willing to spend
on the average, about $2.00 per month ($24.00 per year) for unit
reduction in annoyance due to noise (on the Noise Pollution Ladder)
and on the average, more than $5.50 per month ($66.00 per year)
for noise reduction to a point where noise was never at all an-
noying. On the other hand, the pretest indicated that home owners
176
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Noise Sources
Large Trucks and Buses
Small Trucks
Motorcycles
Sports Cars
Regular Automobiles
Figure 5 .12
Mean Rankings of Five Different Noise Sources by Renters and
Home Owners
Mean
Renters
CO>
3.5
4.1
2.3
4.9
s
Home
Owners
1.4
l'. 3
1.9
1.5
CUP
177
-------
would be willing to spend on the average^less than $.10 per month
($1.00 per year) for unit noise reduction and on the average, $2.50
per month ($30.00 per year) for noise reduction to a level that is
never annoying. However, it should be pointed out that these figures,
particularly those for home owners, are based on very small samples.
Also, the standard deviations of the distributions for renters' and for
home owners' willingness-to-pay for a noise reduction were rather
high. That for renters for a noise reduction to a noise level that
is never at all annoying was 8.6, while that for owners for the same
noise reduction was 10.4. Such large standard deviations are due
basically to the small size of the sample. Nevertheless, it is in-
i teresting that on the average renters are willing to pay more for
tt noise reduction than home owners.
<
5 One explanation of this is that noise is less of a problem to
J home owners than it is to renters since home owners usually live in
less densely populated and thus less noisy areas than renters. Also,
it is suspected that home owners typically having more available in-
come may well have already installed such noise reducing or noise
averting devices as air conditioning or double-pane glass in their
windows. Renters having less available income on the average would
probably have installed fewer noise averting devices than home owners
on the average. Unfortunately, the evidence from the pretest does not
entirely support this hypothesis. More persons who have air condi-
tioning or double-pane glass in their windows would pay nothing for
any noise reduction than would pay something, which tends to support
the hypothesis. But the responses of persons who do not have air
conditioning or double-pane glass indicate that more of them would
178
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also pay nothing for noise reduction than would pay something, which
tends to contradict the hypothesis. The basic reason for this con-
tradictory evidence is probably the small size of the sample.
C. Selection of the Sample to be Interviewed in the Actual Test
The sample of people to be interviewed in the actual administration
of the QEI Noise Pollution Questionnaire should be chosen to live in
geographical clusters. Each respondent should be selected so that he
lives close to fifteen or sixteen other respondents. The purpose of
selecting the respondents from geographical clusters is to permit tests
of differences in individual sensitivity to the same absolute level
of noise. It has been well established that certain people are far
more sensitive to noise than others, and one of the purposes of this
questionnaire is to examine the variability in sensitivity to noise
among individuals. A cluster size of 16 or 17 has been chosen on the
basis of the assumption that there are precisely five levels of sen-
sitivity to noise or five categories of annoyance with noise over which
responses will be normally distributed. A standard statistical
formula was used to calculate the number 16. (See Walpole, Ronald E.,
Introduction to Statistics, Macmillan, New York, 1968, p. 182.)
In addition, the sample of people to be interviewed will be
chosen from areas that are not seriously affected by aircraft or air-
port noise. In this study we wished to avoid overlapping with other
studies on the effects of aircraft and airport noise. Other than
avoiding areas seriously affected by aircraft and airport noise, the
selection of geographical clusters of people to interview should be
performed at random over the entire Boston metropolitan area.
The minimum number of geographical clusters of sixteen persons
179
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each to be interviewed is determined in the following manner. The
income distribution revealed by the pretest indicated that a minimum
of around 62 persons would have to be interviewed to obtain a sample
whose income distribution is identical to that of the entire Boston
metropolitan area. Thus, any constraint imposed by income variability
is obviously not binding, since far more than 62 people must be inter-
viewed in the actual administration of this questionnaire. The principal
constraint determining the size of the sample appears to be the dif-
ficulty in obtaining a good approximation to the distribution of rents.
It seems appropriate to assume that all the members of each geographical
cluster of respondents occupy similar housing. The housing in a geo-
graphical area will certainly not be precisely homogeneous, but should be
similar enough that little harm will be done if it is assumed to be
homogeneous. Thus, it is appropriate to consider the rent distribution
of geographical clusters of homogeneous housing when attempting to
determine the distribution of rents. Assuming the rent distribution to
have seven categories over which clusters of homogeneous housing are
normally distributed, the standard formula used before indicates that
35 geographical clusters are necessary to obtain a good approximation
to the rent distribution. However, not all the housing in any cluster
will be rented homes. Assuming that the pretest ratio of seven
rented homes to five owned homes holds throughout the Boston area,
it appears necessary to interview persons from around 60 geographical
clusters (35 x (1 +•=)). Thus, it appears necessary to interview about
960 people grouped in 60 geographical clusters of 16 people each.
Determining the seasonal period or duration of sampling is a
rather difficult problem. However, since nearly 40% of the people
of this region appear to have air conditioners, selecting the seasonal
180
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period is less critical than it at first appears to be. Only 60% of
the population will be seriously affected by seasonal variations in
the annoyance caused by noise pollution, since the remaining 40%
having air conditioners will be largely shielded from these seasonal
variations in noise. But, seasonal variations in annoyance from noise,
due principally to the increased vulnerability of people to noise
during the summer, is still a serious problem. There appear to be two
possible solutions to this problem: (1) do all the interviewing during
one particular period and then attempt to modify the results to take
account of seasonal variations in noise level, and (2) test the res-
pondents during the fall, winter, or spring and then retest them during
the summer. Both of these methods involve problems, however. As to
method #1, it is difficult to determine precisely how the results of
a survey taken during one season should be modified to account for the
seasonal variations in the effects of noise. The particular survey
results and the direction of modification for taking account of seasonal
variations in noise can indeed be determined, but the precise amounts
of the modifications would be very difficult to estimate. As to method
#2, it would appear to be fairly difficult to combine the information
from a test with that from a retest at a different season on the same
group of respondents. It would be quite difficult to estimate ac-
curately the relative weights to be assigned to the results of the
test and the retest. Information such as the presence or absence
of an air conditioner in the respondent's home and his vacation plans
would have to be included in the estimation of the size of the weights.
Additional research thus must be done on this problem of the seasonal
period of the sampling.
181
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The distributional characteristics of the population to be
sampled, principally the income variability of the population, must
also be considered. However, as indicated before, the variation in
income of the population could be estimated quite well using a sample
of size 61 or 62, whereas we plan to sample about 960 persons, more
than 15 times the number needed to indicate income variability. Other
important distributional characteristics of the population might be
age, commitment to the neighborhood and home ownership. Home ownership
has been specifically included in the calculation of the sample size.
Age and commitment to the neighborhood can both be reduced to variables
having a small number of categories (for the purpose of considering
effects of noise); so therefore, the variability in these factors too
can be taken care of in our rather large sample.
182
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APPENDIX
BIBLIOGRAPHY
A. General Works on Noise
1. Baron, Robert Alex, The Tyranny of Noise, St. Martin's Press, 1970.
2. Beranek, Leo L., ed., Noise and Vibration, McGraw-Hill
A collection of articles on the physics of sound and
vibration and on various devices and structures for
controlling noise.
3. Bragdon, Clifford R., Noise Pollution: The Unquiet Crisis,
University of Pennsylvania Press, 1971.
4. Burns, William, Noise and Man, J.B. Lippincott Company, 1968.
5. Chudnov, V., Noise Abatement, Environmental Protection Agency and
the National Science Foundation, 1974. (Translated from the
Russian. )
6. Informatics, Incorporated, Noise Facts Digest, U.S. Environmental
Protection Agency, Office of Noise Control, June 1972.
Abstracts for numerous papers on various aspects of noise
and a glossary of terms frequently used in scientific
papers on noise.
7. Kryter, Karl D., The Effects of Noise on Man, Academic Press, 1970.
8. National Bureau of Standards, Fundamentals of Noise: Measurement,
Rating Schemes, and Standards, U.S. Environmental Protection
Agency, Office of Noise Abatement and Control, U.S. Govern-
ment Printing Office, Washington, D.C., December 31, 1971.
An introduction to noise, including the inter-relationship
between physical measures of noise and psychological res-
ponses to noise.
9. Richards, E.J., Noise and Society Loughborough University of
Technology (undated manuscript, 18 pages).
An attempt to obtain gross monetary estimates of the benefits
and disbenefits, particularly noise, of airports.
10. Rodda, Michael, Noise and Society, Oliver & Boyd, 1967.
11. Shih, H.H., A Literature Survey of Noise Pollution, NTIS #:
AD-724 344, March 1971.
A compendium of many useful facts about noise and its
effects.
12. Taylor, Robert, Noise, Penguin Books Limited, 1970.
183
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13. U.S. Environmental Protection Agency, Report to the President
and Congress on Noise, U.S. Government Printing Office,
Washington, B.C., 1972.
An introductory presentation of many important facts about
noise and its effects.
14. Yerges, Lyle F., Sound, Noise and VibratJon Control, Van Nostrand
Reinhold Company, 1969.
A discussion of methods for controlling noise, principally
by reducing its intensity during transmission. Appropriate
building design and equipment design to reduce noise pro-
pagation are discussed.
184
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B. Social and Psychological Effects of Noise
1. Abey-Wickrama, I., et al, "Mental Hospital Admissions and Air-
craft Noise", The Lancet, 1969, pp. 1275-1278.
Mental hospital admissions are found to be positively
correlated with high exposure to aircraft noise.
2. Alexandra, Ariel, "The Social Impact of Aircraft Noise", Traffic
Quarterly, 28:3, July 1974, pp. 371-388.
A number of social surveys on the impact of aircraft noise
are summarized and criticized, particularly with regard to
their applicability to public decision making.
3. Bregman, Howard L. and Richard G. Pearson, Development of a Noise
Annoyance Sensitivity Scale, National Aeronautics and Space
Administration, NTIS #: N72-16005, February 1972.
A questionnaire is developed to determine people's psych-
ological reactions to noise in relation to their general
mental outlook.
4. Bryan, Michael, "Noise Laws Don't Protect the Sensitive", New
Scientist, September 27, 1973, pp. 738-740.
5. Cameron, Paul, Donald Robertson, and Jeffry Zaks, "Sound Pollution,
Noise Pollution, and Health: Community Parameters", Journal
of Applied Psychology, 56:1, 1972, pp. 738-740.
Excessive noise exposure is found to be positively correlated
with certain types of chronic and acute illness.
6. Central Institute for the Deaf, Effects of Noise on People,
NTID300.7, U.S. Government Printing Office, Washington, D.C.,
December 31, 1971.
A survey on a large amount of literature on the physical
(basically auditory), psychological and sociological effects
of noise.
7. Crook, M.A. and F.J. Langdon, "The Effects of Aircraft Noise in
Schools Around London Airport", Journal of Sound and
Vibration, 34:2, 1974, pp. 221-232.
The principal effect of aircraft noise on education and class
behavior was found to be interference with speech.
8. Defense Documentation Center, Environmental Pollution: Noise
Pollution - Noise Effects on Human Performance, Volume I of
II Volumes, May 1947 - October 1969, NTIS #: AD729 850,
August 1971.
9. Fidell, Sanford, Glenn Jones, and Karl S. Pearsons, Feasibility of
a Novel Technique for Assessing Noise-Induced Annoyance,
Office of Noise Abatement, Department of Transportation,
NTIS #: PB 225 334, September 1973.
A survey was taken in which participants were given a device
with which they would record incidents of annoyance with noise
as they occurred.
185
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10. Franken, Peter A. and Glenn Jones, "On Response to Community
Noise", Applied Acoustics, 2, 1969, pp. 241-246.
Response to noise was found to be conditioned by past
experience, meaning of the noise, and activity of the
hearer, and was found to be subject to wide variation
between individuals.
11. Glass, David C. and Jerome E. Singer, Urban Stress Experiments
on Noise and Social Stressors, Academic Press, 1972.
12. Glorig, Aram, "Non-Auditory Effects of Noise Exposure", Sound
and Vibration, 5:5, May 1971, pp. 28-29.
13. Griffiths, I.D. and F.J. Langdon, "Subjective Responses to Road
Traffic Noise", Journal of Sound and Vibration, 8,
January 1968, pp. 16-32.
Discussion of the results of an attitudinal survey on noise
and its effects which included a determination of the outside
sound levels near the respondents.
14. Molino, John A., "Equal Aversion Levels for Pure Tones and
1/3-Octave Bands of Noise", Journal of the Acoustical
Society of America, 55:6, June 1974, pp. 1285-1289.
15. National Bureau of Standards, The Social Impact of Noise, U.S.
Environmental Protection Agency, Office of Noise Abatement
and Control, NTID300.il, December 31, 1971.
A short summary of the medical, psychological, and social
effects of noise.
16. Office of Noise Abatement and Control, Information on Levels of
Environmental Noise Requisite to Protect Public Health and
Welfare with an Adequate Margin of Safety, U.S. Environmental
Protection Agency, March 1974.
Derivation of suggested standards for regulating noise to
avoid effects on humans. The appendices contain information
on the effects of noise on health.
17. U.S. Environmental Protection Agency, Public Health and Welfare
Criteria for Noise, Government Printing Office, Washington,
D.C., July 1973.
An examination of 'the effects of noise on physical, physio-
logical and psychological health. The effects of various
types of noise on hearing, speech, sleep, and performance
are discussed.
18. Wyle Laboratories, Community Noise, U.S. Environmental Protection
Agency, Office of Noise Abatement and Control, NTID300.3,
December 31, 1971.
A description of the noise sources and physical measures of
noise in urban areas.
19. Zepler, E.B., et al, "Human Response to Transportation Noise and
Vibration", Journal of Sound and Vibration, 28:3, 1973.,
pp. 375-401.
186
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C. Community Noise
1. Bender, Erich K., "Noise Source Impact In: Construction/Buildings/
Homes", Sound and Vibration, 7:5, May 1973, pp. 33-41.
2. Bishop, Dwight E. and Myles A. Simpson, "Noise Levels Inside and
Outside Various Urban Environments", Sound and Vibration,
8:5, May 1974, pp. 51-54.
A comparison of noise intensity levels inside and outside
various urban environments.
3. Bolt, Beranek, and Newman, Incorporated, Noise Environment of
Urban and Suburban Areas, Federal Housing Administration,
Department of Housing and Urban Affairs, U.S. Government
Printing Office, Washington, D.C., January 1967.
4. Bolt, Beranek, and Newman, Incorporated, Noise from Construction
Equipment and Operations, Building Equipment, and Home
Appliances, U.S. Environmental Protection Agency, Office of
Noise Abatement and Control, NTID300.1, December 31, 1971.
5. Bragdon, Clifford R., "Municipal Noise Ordinances", Sound and
Vibration, 7:12, December 1973, pp. 16-22.
6. Burgasov, P.N., Sanitation Norms of Permissible Noise in Living
Accomodations, Public Buildings, and in the Territory of
Habitable Buildings, National Aeronautics and Space Admin-
istration NASA TT F-15. 065, August 1973. (Translated from
the Russian.)
7. Donley, Ray, "Community Noise Regulation", Sound and Vibration,
3:2, February 1969, pp. 12-21.
8. Galloway, W.J., K.M. Eldred, and M.A. Simpson, Population Distri-
bution of the United States as a Function of Outdoor Noise"
Level. Office of Noise Abatement and Control. U.S. Environ-
mental Protection Agency, November 1973.
Increasing population density is found to have a strong
positive correlation with noise intensity level.
9. Gebman, Jean R., The Mechanics of Forecasting the Community Noise
Impact of a Transportation System, NTIS #: AD-737 684,
November 1971.
The mechanics of determining the number of people affected
by the noise from a new urban transportation system.
10. George Washington University, Laws and Regulatory Schemes for
Noise Abatement, NTID300.4, U.S. Government Printing Office,
Washington, D.C., December 31, 1971.
187
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11. Morse, Kenneth M., "Community Noise - The Industrial Aspect",
American Industrial Hygiene Association Journal. 29
July-August 1968, pp. 368-380.
A discussion is presented of community noise with emphasis
on noise rating schemes.
12. Noise Abatement Group, Transportation Systems Center, U.S.
Department of Transportation, A_Community Noise Survey
of Medford, Massachusetts, Office of Noise Abatement,
U.S. Department of Transportation, NTIS #: PB-211 975,
August 1971.
A presentation of the actual noise levels occurring at
various sites in a suburb of Boston.
13. Senko, Alexander and Palghat W. Krishman, L.S. Goodfriend and
Associates, Urban Noise Survey Methodology (two volumes),
New York City Department of Air Resources Environmental
Protection Administration, Bureau of Noise Abatement and
U.S. Department of Housing and Urban Development, Office
of Research and Technology, November 1971.
A description of the methodology for taking a noise level
survey on a large urban area.
14. Wyle Research Staff, A Program for the Measurement of Environmental
Noise in the CommunityandItsAssociated Human Response,
Volume 1 - A Feasibility Test of Measurement Techniques"
Office of Noise Abatement, Department of Transportation,
NTIS #: PB 228 563, December 1973.
15. Wyle Research Staff, A Program for the Measurement of Environmental
Noise in the Community and Its Associated Human Response,
Volume II - A Plan for a National Program, Office of Noise
Abatement, Department of Transportation, NTIS #: PB 228 564,
December 1973.
A questionnaire on attitudes toward noise is developed,
justified, and presented in the two above references.
188
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D. Highway Noise (See also listings under "economic studies")
1. Anderson, Grant S., Frederick Gottemoeller, and Daniel G. Page,
"Baltimore Plans Highway for Minimum Noise", Civil Engineer-
ing-ASCE, September 1972, pp. 74-78.
2. Beaton, John L. and Louis Bourget, Can Noise Radiation from High-
ways be Reduced by Design?, State of California Highway
Transportation Agency, January 1968.
A discussion of the results of several empirical studies
on the effect of design on freeway noise radiation.
3. Burt, M.E., Roads and the Environment, NTIS, 1972.
A discussion of the adverse efforts of traffic noise on
the environment.
4. Chalupnik, James D., ed., Transportation Noises: A Symposium on
Acceptability Criteria, University of Washington Press, 1970.
A Collection of articles on transportation noise and its
effects including laboratory and survey methods of evaluating
human responses to noise.
5. Consultative Group on Transportation Research, Urban Traffic
Noise, Organization for Economic Cooperation and Develop-
ment, 1971.
6. Galloway, William J., and Glenn Jones, Motor Vehicle Noise -
Identification and Analysis of Situations Contributing to
Annoyance, Society of Automotive Engineers, Automotive
Engineering Congress, Detroit, Michigan, January 10-14, 1972.
The results of an analysis performed on interviews on an-
noyance due to motor vehicle noise.
7. Galloway, William J., Welden E. Clark, and Jean S. Kendrick,
Highway Noise Measurement, Simulation, and Mixed Reactions,
Highway Research Board, Division of Engineering, National
Research Council, National Academy of Sciences - National
Academy of Engineering, 1969.
8. Gordon, Colin G., et al, Highway Noise: A Design Guide for
Highway Engineers, National Cooperative Highway Research
Program Report 117, Highway Research Board Division of
Engineering, National Research Council, National Academy
of Sciences - National Academy of Engineering, 1971.
9. Grove, G.H., Simplified Technique for Traffic Noise Level
Estimation, Michigan State Highway Commission, April 1973.
10. Lyon, Richard H., Lectures in Transportation Noise, Grozier,
Cambridge, Mass., 1973.
A discussion of the production and propagation of noise
produced by various types of transportation vehicles -
aircraft, trucks and automobiles, and railroad and subway
trains. Formulas are presented for calculating noise levels
in certain situations.
189
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11. Michigan Department of State Highways, Pollution of Michigan
Urban Atmosphere by Highway-Generated Noise, Michigan State
Highway Commission, February 1973.
12. Miller, Stanley F., Jr., Effects of Proposed Highway Improvements
on Property Values, National Cooperative Highway Research Pro-
gram Report 114, Highway Research Board, Division of Engineer-
ing, National Research Council, National Academy of Sciences -
National Academy of Engineering, 1971.
13. Nelson, K.E. and T.D. Wolsko, Transportation Noise: Impacts and
Analysis Techniques, Argonne National Laboratory, NTIS #:
PB-226 806, October 1973.
The effects of urban noise are discussed and a highway
noise model is presented.
14. Serendipity, Incorporated, A Study of the Magnitude of Transporta-
tion No ige Generation and Potential Abatement Volume IV -
Motor Vehicle/Highway System Noise Final Report, Department
of Transportation, Office of Noise Abatement, NTIS #:
PB 203 185, November 1970.
A model for highway noise is presented and various methods
for abatement are discussed. The noise produced by various
vehicle types is also analyzed.
15. Waller, R.A., Evaluation of the Impact of New Roads, Atkins
Research & Development, Epsom, Surrey, August 1973, 19 pp.
16. Wyle Laboratories, Transportation Noise and Noise from Equipment
Powered by Internal Combustion Engines, U.S. Environmental
Protection Agency, Office of Noise Abatement and Control,
NTID300.13, December 31, 1971.
The levels of noise produced by various types of vehicles
are discussed and analyzed.
190
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E. Aircraft Noise (See also listings under "economic studies")
1. Bolt, Beranek, and Newman," Incorporated, Land Use Planning
Relating to Aircraft Noise, October 1964.
2. Branch, Melville C., Outdoor Noise and the Metropolitan Environ-
ment Case Study of Los Angeles with Special Reference to
Aircraft, Department of City Planning, Los Angeles, Califor-
nia, 1970.
3. Environmental Protection Agency, Report on Aircraft - Airport Noise,
Report to Congress, July 1973.
A discussion of the adequacy of FAA flight and operational
noise controls and noise emission standards for new aircraft.
4. Franken, Peter A. and David Standley, Aircraft Noise and Airport
Neighbors: A Study of Logan International Airport, Prepared
for Department of Transportation and Department of Housing
and Urban Development, Report No. DOT/HUD IANP-70-1, March
1970.
This paper includes a discussion and analysis of public
complaints about the noise produced by Logan Airport.
5. Haar, Charles M., "Airport Noise and the Urban Dwellers: A Pro-
posed Solution", The Appraisal Journal, October 1968,
pp. 551-558.
6. Plessas, Demetrius J., "Airport Noise: Some Perspectives", Land
Economics, 1973, pp. 14-21.
7. Richards, E.J. and J.B. Ollerhead, "Noise Burden Factor - New Way
of Rating Airport Noise", Sound and Vibration, 7:12, Decem-
ber, 1973, pp. 31-33.
8. Rylander, R., Sorensen, S. and A.Xajland, "Annoyance Reactions
from Aircraft Noise Exposure", Journal of Sound and Vibration,
1972, 24:4, pp. 419-444.
The results of a survey on people's annoyance with aircraft
noise.
191
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F. Economic Studies on Noise Disturbance
1. Anderson, R.J., Jr. and T.D. Crocker, "Air Pollution and Property
Values: A Reply", The Review of Economics and Statistics,
1972, pp. 470-473.
2. Anderson, R.J., Jr. and T.D. Crocker, "Air Pollution and Residential
Property Values", Urban. Studies", October 8, 1971, pp. 171-180.
3. Bain, Joe S., "Some Environmental Impacts of our Freeway and Airline
Transportation Systems", (Chapter 8), Environmental Decay:
Economic Causes and Remedies, Little Brown, and Company, 1973.
4. Colony, David C., Expressway Traffic Noise and Residential Pro-
perties, State of Ohio, Department of Highways and U.S.
Department of Transportation, Bureau of Public Roads, NTIS #:
PB 183 903, July 1, 1967.
5. DeVany, Arthur, "The Measurement and Cost of Airport Noise",
Presented at the Conference on Externalities, Southern
Illinois University at Edwardsville.
Alternative models of the effect of airports and aircraft
on the environment in residential areas are presented along
with mean values of housing in affected areas.
6. Emerson, Frank C., "The Determinants of Residential Value with
Special Reference to the Effects of Aircraft Nuisance
and Other Environmental Features", University of Minnesota
Ph.D. Dissertation, April 1970, University Microfilms.
7. Emerson, Frank C., "The Valuation of Residential Amenities: An
Econometric Approach", The Appraisal Journal, April 1972,
pp. 268-278.
8. Feller, Irwin and Jon P. Nelson, Economic Aspects of Noise Pollution,
The Pennsylvania State University Institute for Research on
Human Resources, Center for Study of Science Policy, April 1973.
A microeconomic analysis of noise and its effects plus an
evaluation of several empirical studies on the effects of noise
and air pollution on property values.
9. Foster, C.D. and P.J. Mackie, "Noise: Economic Aspects of Choice",
Urban Studies, June 1970, pp. 123-125.
An overview of alternative methods of reducing or preventing
noise including estimates of costs of each method.
10. Freeman, A.M., Ill, "Air Pollution and Property Values: A Method-
ological Comment", The Review of Economics and Statistics,
November 1971, pp. 425-426.
11. Goldberg, Stanley R., "A Cost-Effective Method of Evaluating Aircraft
Noise Abatement Options", Texas Business Review, 47:12,
December 1973, pp. 1-4.
192
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12. Goodfriend-Ostergaard Associates, Metropolitan Noise Abatement
Policy Study, John F. Kennedy International Airport. New York.
New York: Technical Supplement. Noise Reducing Constructions
and Cost Estimating in High Noise Areas, Tri State Trans-
portation Commission, New York, New York, NTIS #: PB 199 724,
February 1970.
13. Lehmann, Edward J., Pollution Economics. 1970 through 1973. A
Bibliography with Abstracts, NTIS-ffIN-73-008, July 1973.
14. Loucks, Daniel P., Blair T. Bower, and Walter 0. Spofford, Jr.,
"Environmental Noise Management", Journal of the Environmental
Engineering Division, December 1973, pp. 813-829.
A discussion of the problem of controlling noise in the environ-
ment including some recommended noise standards.
15. McClure, Paul T., Indicators of the Effect of Jet Nnisp on the
Value of Real Estate. The RAND Corporation, July 1969.
16. McClure, Paul T., Some Projected Effects of Jet Noise on Residential
Property Near Los Angeles International Airport by 1970. The
RAND Corporation.
17. Mishan, E.J., "The Economics of Disamenity", Natural Resources
Journal, 14, January 1974, pp. 55-86.
18. National Bureau of Standards, The Economic Impact of Noise, U.S.
Environmental Protection Agency, Office of Noise Abatement
and Control, Government Printing Office, NTID300 14,
December 31, 1971.
A general discussion of the problems of determining the costs
of aircraft noise, ground transportation noise, and internal
home noise.
19. Nelson, Jon P., The Effects of Mobile-Source Air and Noise Pollution
on Residential Property Values. Department of Transportation,
January 1975.
This reference includes a section on the effects of motor-
vehicle traffic noise on residential property values, along
with chapters on the effects of air pollution and jet aircraft
noise on residential property values.
20. Nwaneri, V.C., "Equity in Cost-Benefit Analysis: A Case Study of
The Third London Airport", Journal of Transport Econnmir-.s and
Policy, 4:3, September 1970, pp. 235-254.
21. Paik, Inja Kim, Impact of Transportation Noise on Urban Resident, ia.1
Property Values with Special Reference to Aircraft Nnisp,
Urban Transportation Center Consortium of Universities, NTIS #:
PB 194 .101, August 1970.
A regression model of the impact of transportation noise on
urban residential property values.
193
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22. Paul, M.E., "Can Aircraft Noise Nuisance Be Measured in Money?",
Oxford Economic Papers, 1971, pp. 297-322.
23. Pearce, David, "The Economic Evaluation of Noise-Generating and
Noise Abatement Projects", in Problems of Environmental
Economics, Organization for Economic Cooperation and
Development, 1972, pp. 103-118.
24. Randall, Alan, Berry C. Ives, and Clyde Eastman, "Benefits of
Abating Aesthetic Environmental Damage from the Four Corners
Power Plant, Fruitland, New Mexico,"Bulletin 618, Agricultural
Experiment Station, New Mexico State University, May 1974.
25. Ridker, R.B. and J.A. Henning, "The Determinants of Residential
Property Values with Special Reference to Air Pollution",
The Review of Economics and Statistics, May 1967, pp. 246-257.
26. Robin M. Towne and Associates, Incorporated, An Investigation of
the Effect of Freeway Traffic Noise on Apartment Rents,
Oregon State Highway Commission, State Highway Department and
the U.S. Department of Commerce, Bureau of Public Roads,
NTIS #: PB 176 44, October 1966.
27. Safeer, Harvey B., "Aircraft Noise Reduction - Alternatives Versus
Cost", Sound and Vibration. 7:10, October 1973, pp. 22-27.
28. Seneca, Joseph J. and Michael K. Taussig, Environmental Economics.
Prentice-Hall, Incorporated, Englewood Cliffs, New Jersey, 1974,
While this book is basically concern-ed with the economics of
other environmental problems, it does include a short non-
technical section on noise.
29. Starkie, D.N.M. and D.M. Johnson, "Exclusion Facilities and the
Valuation of Environmental Goods", Centre for Environmental
Studies, Urban Economics Conference 10-13 July 1973, Centre
for Environmental Studies, 5 Cambridge Terrace, Regent's
Park London NW1 4JL.
This paper presents a method for evaluating the cost of noise
or some other environmental good by considering its relation-
ship to exclusion facilities, such as double-pane glass.
30. Starkie, D.N.M. and D.M. Johnson, "Loss of Residential Amenity:
An Extended Cost Model", Regional Studies. 7, 1973,pp. 177-181.
31. Thomas, R.J., "Traffic Noise - The Performance and Economics of
Noise Reducing Materials", Applied Acoustics. 2, 1969,
pp. 207-213.
32. Waller, R.A., "Economics of Sound Reduction in Buildings", Applied
Acoustics. 1968, pp. 205-213.
The costs of both noise-attenuating and noise-absorbing
materials are discussed, along with methods for optimizing
noise reduction per dollar spent.
194
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33. Waller, Roy and Robert Thomas, "The Cash Value of the Environment",
Arena, Architectural Association Journal, 82:908, January 1967,
pp. 164-166.
34. Walters, A.A., "Mrs Paul on Aircraft Noise - A Correction", Oxford
Economic Papers, 1972, pp. 287-288.
35. Yerges, Lyle F., "Cost/Effectiveness Approach to Machinery Noise
Control", Sound and Vibration, 8:7, July 1974, pp. 30-32.
195
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G. General Works on Environmental Economics and the Theory
of Public Goods
1. Aaron, H. and M. McGuire, "Efficiency and Equity in the
Optimal Supply of a Public Good", Review of
Economics and Statistics, 51, 1969, pp. 31-39.
2. ABT Associates, Incentives to Industry for Water Pollution
Control, 1967.
3. Ackerman, B. and Sawyer, "The Uncertain Search for Environ-
mental Policy, Scientific Factfinding and Rational
Decision Making Along the Delaware River", University
of Pennyslvania Law Review, 20, 1973.
4. Arrow, K.J., "The Organization of Economic Activity: Issue
Pertinent to the Choice of Market vs. Nonmarket Allo-
cation", in Haveman, R.H. and Margolis, J. (eds), Public
Expenditures and Policy Analysis, Markham Publishing
Company, 1970, pp. 59-73.
5. Arrow, K.J., Social Choice and Individual Values, 2nd edition,
John Wiley, New York, 1964.
6. Arrow, K.J. and T. Scitovsky, eds., Readings in Welfare
Economics, Irwin, Homewood, Illinois, 1969.
7. Ayres, Robert U. and Allen V. Kneese, "Production, Consumption
and Externalities", The American Economic Review, 59,
June 1969, pp. 282-297.
8. Bain, J.S., Environmental Decay, Little Brown, 1973.
9. Bator, Francis M., "The Anatomy of Market Failure", The
Quarterly Journal of Economics, 72, August 1958, pp. 351-379.
10. Michael Baker, Incorporated, Analysis of Pollution Control
Costs, prepared for the Appalachian Regional Commission,
February 1973.
On coal mining problems.
11. Baumol, W.J., "External Economies and Second-Order Optimality
Conditions", American Economic Review, 54, June 1964,
pp. 358-372.
12. Baumol, W.J., "On Taxation and the Control of Externalities",
American Economic Review, 63:3, June 1972.
An analysis of the difficulties of designing tax policies
consistent with Pareto efficient resource allocation
conditions.
196
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13. Baumol, W.J. and D.F. Bradford, "Optimal Departures from
Marginal Cost Pricing", American Economic Review, 60:3,
June 1970, pp. 265-284.
14. Baumol, W.J. and W.E. Dates, "The Use of Standards and Prices
to Protect the Environment", The Swedish Journal of
Economics, 73, March 1971, pp. 42-54.
15. Baumol, W.J. and R.E. Quandt, "Rules of Thumb and Optimally
Imperfect Decisions", American Economic Review, 54:1,
May 1964, pp. 44-52.
On the imperfect choice of imperfect decision rules.
16. Bergson, A., "A Reformulation of Certain Aspects of Welfare
Economics", Quarterly Journal of Economics, 52, February
1938, pp. 310-334.
17. Black, R., A. Muhieh, et al, The National Solid Waste Survey,
U.S. Department of Health, Education, and Welfare,
Washington, D.C., October 24, 1968.
18. Bohn, P. and A.V. Kneese (eds), The Economics of Environment,
Macmillian, London, 1971.
19. Bower, B.T. and A.V. Kneese, Managing Water Quality, Johns Hopkins
Press, Baltimore, Maryland, 1968.
A discussion of experience with effluent charges and
standards.
20. Buchanan, James M., "The Coase Theorem and the Theory of the
State", Natural Resources Journal, 13, October 1973, pp. 579-594.
21. Buchanan, James M., The Demand and Supply of Public Gcods,
Rand McNally, 1969.
22. Buchanan, James M.,"External Diseconomies, Corrective Taxes and
Market Structure", American Economic Review, 59, March 1969,
pp. 174-177.
23. Buchanan, James M., "Politics, Policy and the Pigovian Margins",
Economica. N.S. 29, February 1962, pp. 17-28.
24. Buchanan, James M., "Positive Economics, Welfare Economics, and
Political Economy", Journal of Law and Economics, 2, October
1959, pp. 124-138.
25. Buchanan, James M. and W.C. Stubblebine, ''Externality", Economica,
29, November 1962, pp. 371-384.
26. Burrows, Paul, "On External Costs and the Visible Arm of the Law".
Oxford Economic Papers, 22, March 1970, pp. 39-56.
27. Calabresi, G., The Costs of Accidents: A Legal and Economic
Analysis, Yale University Press, 1970.
197
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28. Chase, Samuel B., ed., Problems in Public Expenditure Analysis,
The Brookings Institution, 1966.
29. Clawson, M. and J.L. Knetch, The Economics of Outdoor Recreation,
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30. Coase, R., "The Nature of the Firm", Economica, 4, November 1957,
pp. 386-405.
31. Coase, R., The Problem of Social Cost", Journal of Law and
Economics, 3, October 1960, pp. 1-44.
32. Commoner, Barry, The Closing Circle, Nature, Man and Technology,
Alfred A. Knopf, New York, 1971.
33. Conner, J.R. and E. Loehman, eds., Economic Decisionmaking for
Environmental Control, Gainesville,1973.
34. Council on Environmental Quality, Second Annual Report, Environmental
Quality, Government Printing Office, Washington, B.C., August
1971.
35. Crowe, Beryl L., "The Tragedy of the Common Revisited", Science, 166,
November 28, 1969, pp. 1103-1107.
36. Dahmen, Erik, "Environmental Control and Economic Systems", The
Swedish Journal of Economics, 75, March 1971, pp. 67-75.
37. Dales, J.H., Pollution, Property and Prices, An Essay in Policy-
making and Economics, University of Toronto Press, Toronto, 1968.
38. D'Arge, Ralph C., "Essay on Economic Growth and Environmental
Quality, Swedish Journal of Economics, 73, March 1971, pp. 25-41.
39. Davidson, Paul, F.^Gerard Adams, and Joseph Seneca, "The Social
Value of Water Recreational Facilities Resulting from an
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40. Davis, O.A. and M.I. Kamien, "Externalities, Information and Al-
ternative Collective Action", The Analysis and Evaluation of
Public Expenditures: The PPB System, Joint Economic Com-
mittee, 91st Congress, 1st Session, Government Printing
Office, Washington, D.C., 1969.
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41. Davis, O.A. and A.B. Whinston, "Externalities, Welfare, and the
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1962, pp. 241-262.
42. Davis, O.A. and A.B. Whinston, I10n Externalities, Information, and
the Government-Assisted Invisible Hand", Economica, 33,
August 1966, pp. 303-318.
198
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43. O.A. Davis and A.B. Whinston, "Some Notes on Equating Private
and Social Cost", Social Economics Journal, 32, October
1965, pp. 113-126.
44. Davis, R.K., The Range of Choice in Water Management: A Study
of Dissolved Oxygen in the Potomac Estuary, Johns Hopkins
Press for Resources for the Future, 1968.
45. Day, H.J., F.T. Dolbear, and M. Kamien, "Regional Water Quality
Management - A Pilot Study", Proceedings of the First Annual
Meeting of the American Water Resources Association, 1965,
pp. 283-309.
46. Debreu, Gerard, Theory of Value, Wiley, 1959.
47. Demsetz, H. , "The Exchange and Enforcement of Property Rights",
Journal of Law and Economics, 7, October 1964, pp. 11-26.
48. Dolan , Edwin G. , TANS-TAAFL, The Economic Strategy for Environmental
Crisis, Holt, Reinhart, and Winston, Incorporated, New York,
1971.
49. Dolbear, F.T., "On the Theory of Optimal Externality", The
American Economic Review, 57, March 1967, pp. 90-103.
50. Dorfman, Robert, ed. , Measuring Benefits of Government Investment,
The Brookings Institution, 1965.
51. Dorfman, Robert and Nancy S. Dorfman, eds., Economics of the
Environment. W.W. Norton & Company, Incorporated, 1972.
52. Dorfman, R. , Jacoby, H.D., and Thomas, H.A., Jr., eds., Models
for Managing Regional Water Quality, Harvard University
Press, 1972.
53. Eckstein, Otto, "A Survey of the Theory of Public Expenditures
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54. Energy Policy Project, Interim Report, Washington, February 1974.
55. Energy Policy Staff, Office of Science and Technology, Electric
Power and the Environment, Government Printing Office,
Washington, D.C., 1970.
A discussion of the environmental problems associated with
electrical power generation.
56. Ethridge, D. , "User Charges as a Means for Pollution Control",
Bell Journal of Economics and Management Science, 3:1,
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199
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57. Fabricant, Neil and Robert M Hallman, Toward a Rational Power
Policy, Energy, Politics and Pollution, a Report of the
Environmental Protection Agency of the City of New York,
George Braziller, New York,1971.
58. Fair, G.M., J.C. Geyer, and D.A. Okun, Water and Wastewater
Engineering, 2, pp. 33-45.
59. Fredickson, H.G. and H. Magnus, "Comparing Attitudes Toward Water
Pollution in Syracuse", Water Resources Research, 14, October
1968, pp. 877-889.
60. Freeman, A.M., Ill, and R.H. Haveman, "Clean Rhetoric and Dirty
Water", The Public Interest, Summer 1972.
Critical analysis of the 1972 Water Pollution Control Act.
61. Freeman, A.M., Ill, and R.H. Haveman, "Residual Charges for Pol-
lution Control: A Policy Evaluation",Science, 174.
62. Freeman, A.M., Ill, R.H. Haveman, and A.V. Kneese, The Economics
of Environmental Policy, Wiley, 1973.
63. Goldman, M.I., "Pollution: The Mess Around Us", in Ecology and
Economics: Controlling Pollution in the 70's, Prentice-
Hall, Incorporated, Englewood Cliffs, New Jersey, 1972.
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64. Graaff, J. de V., Theoretical Welfare Economics, Cambridge, 1957.
65. Greco, J. and W.A. Wynot, "Operating and Maintenance Problems
Encountered with Electrostatic Precipitators", presented
to the American Power Conference, April 20, 1971, Tennessee
Valley Authority.
66. Grilliches, Z., "Comment", in The Rate and Direction of Inventive
Activity, National Bureau of Economic Research and Princeton
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67. Hardin, Garrett, "The Tragedy of the Common", Science, 162,
December 13, 1968, pp. 1243-1248.
68. Harsanyi, J. , "Welfare Economics of Variable Tastes", Review of
Economic Studies, 21, 1953-1954, pp. 204-213.
69. Haveman, R.H. and J. Margolis, eds., Public Expenditures and
Policy Analysis, Markham Publishing Company, Chicago, 1970.
70. Hay, G.A., "Import Controls on Foreign Oil: Tariff or Quota?",
American-Economic Review, 61, September 1971, pp. 688-691.
71. Head, J.G., "Public Good and Public Policy", Swedish Journal of
Economics, 70, March 1971.
72. Herfindahl, Orris C., and Allen V. Kneese, Quality of the Environ-
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200
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73. Jacoby, Henry and John D. Steinbruner, Clearing the Air,
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74. Jarrett, Henry, ed., Environmental Quality, Johns Hopkins Press,
Baltimore, Maryland, 1966.
75. Johnson, E.L., "A Study in the Economics of Water Quality Manage-
ment", Water Resources Research, 3:2, 1967, pp. 297ff.
76. Jones, Fish and River Pollution, Buttersworth, London, 1969.
77. Joskow, P., "Approving Nuclear Power Plants: Scientific Decision
Making or Administrative Charade", Bell Journal of Economics
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78. Kamien, M.I., N.L. Schwartz, and F.T. Dolbear, "Asymmetry between
Bribes and Charges", Water Resources Research, First Quarter,
2, 1966, pp. 147-157.
79. Kerri, K.D., "An Economic Approach to Water Quality Control",
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December 1966, pp. 18-83.
80. Kneese, Allen V., The Economics of Regional Water Quality
Management, Baltimore, 1964.
81. Kneese, Allen V., "Environmental Economics and Policy", The
American Economic Review,61, May 1971, pp. 153-166.
82. Kneese, Allen V., Robert U. Ayres, and Ralph C. D'Arge, Economics
and the Environment: A Materials Balance Approach, Johns
Hopkins Press, Baltimore, Maryland, 1970.
83. Kneese, Allen V. and B.T. Bower eds., Environmental Quality
Analysis, Johns Hopkins Press, Baltimore, Maryland, 1972.
84. Kneese, Allen V. and B.T. Bower, Managing Water Quality: Economics,
Technology, Institutions, Johns Hopkins Press, Baltimore,
Maryland, 1968.
85. Krutilla, John, "Conservation Reconsidered", The American Economic
Review, 57, September 1967, pp. 777-786.
86. Krutilla, John, "Some Environmental Effects of Economic Develop-
ment", Daedalus, Fall 1970, pp. 1058-1070.
87. Landsberg, Hans H., "The U.S. Resource Outlook, Quantity and
Quality", Daedalus, Fall 1967, pp. 1034-1057.
88. Lansing, John B. and James N. Morgan, Economic Survey Methods,
I.S.R., University of Michigan, 1973.
89. Lave, L. and E. Seskin, "Air Pollution and Human Health", Science,
169, August 21, 1970, pp. 723-733.
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90. Lave, Lester B. and Eugene P. Seskin, "Health and Air Pollution",
The Swedish Journal of Economics, 73, March 1971, pp. 76-95.
91. Leavitt, J.M., S.B. Carpenter, J.P. Blackwell, andT.L.
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Plant Stack Emissions", Journal of the Air Pollution
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92. Leibenstein, H., "Allocative Efficiency vs. X-Efficiency", The
American Economic Review, 56, June 1966, pp. 392-415.
93. Lipsey, R.G. and K. Lancaster, "The General Theory of Second
Best", Review of Economic Studies, 24, 1956, pp. 11-32.
94. Little, I.M.D., A Critique of Welfare Economics, second edition,
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95. McKean, Roland, "The Unseen Hand in Government", The American
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96. McKean, Roland, "Property Rights Within Government and Devices
to Increase Governmental Efficiency", Southern Economic
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97. Maas, Arthur, "Benefit Cost Analysis - Its Relevance for Public
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98. Maas, A., et al, Design of Water Resource Systems, Harvard
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99. Meade, James E.,"External Economies and Diseconomies in a
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100. Meade, James E., The Theory of Economic Externalities, Leiden:
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101. Michelman, F.J., "Pollution as a Tort: A Non-accidental Per-
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1971, pp. 647-686.
102. Michelman, F.J., "Property Utility, and Fairness: Comments on the
Ethical Foundations of 'Just Compensation' Law", Harvard
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103. Mishan, E.J., Cost Benefit Analysis, Praeger, 1973.
104. Mishan, E.J., "Pangloss on Pollution", The Swedish Journal of
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105. Mishan, E.J., "Pareto Optimality and the Law", Oxford Economic
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202
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106. Mishan, E.J., "Reflections on Recent Developments in the
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107. Mishan, E., "Second Thoughts on Second Best," Oxford Economic
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108. Mishan, E.J., Technology and Growth, The Price We Pay, New
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109. Mishan, E. J., "Welfare Criteria for External Effects," Ameri-
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110. Mohring, H. and J. H. Boyd, "Analyzing 'Externalities': Direct
Interaction vs. Asset Utilization Frameworks", Economica, 1972.
111. Montgomery, W.D., "Markets in Licenses and Efficient Pollution
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112. Musgrave, R.A., ed., Broad-Based Taxes, Johns Hopkins Press, 1973.
113. Musgrave, Richard A. and Peggy B. Musgrave, Public Finance in
Theory and Practice, McGraw-Hill, 1973.
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114. Musgrave, R. and A. Peacock, eds., Classics in the Theory of
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115. National Academy of Sciences, The Committee on Pollution.
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116. Nutter, G. W., "The Coase Theorem on Social Cost," Journal of
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117. Olsen, M., The Logic of Collective Action, Harvard University
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118. Olson, Mancur, Jr. and Richard Zeckhauser, "Collective Goods,
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119. Peterson and. Etter, A Background for Disturbed Land Reclamation
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120. Oster, S., "The Benefits and Costs of Water Pollution Control:
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On the way local governments adjust to pay for pollution
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203
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121. Perloff, Harvey S., ed., The Quality of the Urban Environment,
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122. Pigou, A.C., The Economics of Welfare, 4th ed., London: Mac-
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123. President's Science Advisory Committee, Environmental Panel,
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124. Prest, A. R. and Ralph Turvey, "Cost-Benefit Analysis: A Survey,"
The Economic Journal, 74, December 1965, pp. 683-735.
125. Reich, Charles A., "The New Property," Yale Law Journal, 73,
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126. Rees, R., "Second-Best Rules for Public Enterprise Pricing,"
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127. Ridker, Ronald G., Economic Costs of Air Pollution, New York:
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128. Roberts, M.J., "Alternative Social Choice Criteria, a Normative
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129. Roberts, M.J., "Comment," American Economic Review, May, 1971.
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131. Roberts, M.J., "A Framework for Analyzing the Behavior of Resource-
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132. Roberts, M.J., "Study of the Measurement and Distribution of
the Costs and Benefits of Water Pollution Control,"
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133. Roberts, Marc J., "Organizing Water Pollution Control: The
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134. Rockafeller, R. T., Convex Analysis, Princeton, N.J.: Princeton
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135. Rothenberg, Jerome, "The Economics of Congestion and Pollution."
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137. Samuelson, P.A., "Diagrammatic Exposition of a Theory of Public
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141. Samuelson, P.A., "Social Indifference Curves," Quart. Jour. Econ.
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142. Sax, J. L., Defending the Environment, Knopf, 1970.
143. Schelling, Thomas C., "On the Econogy of Micromotives," The
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144. Scitovsky, Tibor, "External Diseconomies in the Modern Economy,"
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148. Seneca, Joseph J. and Michael K. Taussig, Environmental Economics,
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149. Sewell, W.R.D. and I. Burton, eds., Perceptions and Attitudes
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150. Shapley.L. and M. Shubik, "On the core of an economic system
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158. Summers, W., Pollution Control in the Paper Industry , unpub-
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161. Taxation with Representation, The Proposed Tax on Sulfur
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/5-76-002
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
Economic Welfare Impacts of Urban Noise
5. REPORT.DATE
May 1976 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Rodney Thorpe
Thomas Holmes
8. PERFORMING ORGANIZATION REPORT NO.
5531
9. PERFORMING ORGANIZATION NAME AND ADDRESS
QEI, Inc.
119 The Great Road
Bedford, Ma. 07130
10. PROGRAM ELEMENT NO.
1HA094
11. CONTRACT/GRANT NO.
68-01-2634
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Health and Ecological Effects
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
13. TYPE OF REPORT AND PERIOD COVERED
Project, ending 5/15/75
14. SPONSORING AGENCY CODE
EPA-ORD
16. SUPPLEMENTARY NOTES
16. ABSTRACT
The basic purpose of this project was to develop a conceptual framework for
estimating the social welfare gains or benefits of reducing current noise
levels in urban environments. The project has concentrated on developing economic
welfare theory and empirical techniques to assess willingness-to-pay by
individuals for noise avoidance. Particular attention was paid to noise produced
by motor vehicles and noise produced by operations at construction sites.
The theoretical effect of the localized nature of noise on people's
willingness-to-pay to control noise was investigated and found to be important.
An efficient pricing scheme for aggregate noise disturbance was devised, based
on people's willingness-to-pay for noise reduction. A systematic analysis of
the case of many suppliers of the public good of noise reduction was carried out.
A questionnaire was developed to elicit responses on the physical and
psychic costs of noise in urban areas. This questionnaire will attempt to
assign dollar values to the costs of noise pollution by determining people's
willingness-to-pay to control or reduce noise.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COS AT I Field/Group
Noise (sound)
Economic surveys
Economic analysis
Noise reduction
Transportation noise
Willingness-to-pay
Pollution abatement
benefits
Economic efficiency
20A
5C
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
216
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
208
OUSGPO: 1976 — 657-695/5433 Region 5-1
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EPA-335
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