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Negative Externalities
David Levinson
Motivation
• To measure externalities as a function
of usage
• To enable the evaluation of the “Full
Cost” of different modes under different
circumstances
• To measure the costs consistently (in
$/pkt) to compare fairly
Overview
• What are externalities
• Key Issues
• Our approach to the problem
• Cost by cost discussion
• Summary
Private Cost vs. Social
Cost
• The purpose of • The difference between
distinguishing private and private and social cost is that
social cost is to correct for in making a decision a
real resource misallocation private individual will take
from economic agents account of the costs they
actions which impose a cost face but will not consider the
(or benefit) on others in the impact of their decision on
market. The market provides others which may, in fact.
no incentive for agents to impose a cost upon them. If
take account of their actions. this occurs an externality will
misallocate resources since
the economic agents is not
forced to pay the cost they
impose or does not receive
any compensation for the
benefits which they confer.
Externality
• An externality is that situation in • Examples:
which the actions of one agent
imposes a benefit or cost on – negative externalities
another economic agent who is (external disbenefits) are
not party to a transaction. air pollution, water
• Externalities are the difference pollution, noise,
between what parties to a
transaction pay and what congestion.
society pays – positive externalities
• A pecuniary externality, (external benefits) are
increases the price of a bees from apiary
resource and therefore involves
only transfers, pollinating fruit trees and
• A technical externality exhibits a orchards supplying bees
real resource effect. A technical with nectar for honey.
externality can be an external
benefit (positive) or an external
disbenefit (negative).
Source of the Problem
• The source of externalities is • We want that amount of the
the poorly defined property externality which is only
rights for an asset which is worth what it costs.
scarce. For example, no one Efficiency requires that we
set the price of any asset >0
owns the environment and so the externality is
yet everyone does. Since no internalized. If the price is
one has property rights to it, set equal to the marginal
no one will use it efficiently social damages, we will get
and price it. Without prices a socially efficient amount of
people treat it as a free good the good or bad. Economic
and do not cost it in their agents will voluntarily abate
decision making. Overfishing if the price is non-zero.
can be explained in the
same way.
Coase Theorem
• The Coase Theorem states that in the
absence of transaction costs, all
allocations of property are equally
efficient, because interested parties will
bargain privately to correct any
externality. As a corollary, the theorem
also implies that in the presence of
transaction costs, government may
minimize inefficiency by allocating
property initially to the party assigning it
the greatest utility.
Pareto Optimality
• A change that can make at least one
individual better off, without making any
other individual worse off is called a
Pareto improvement: an allocation of
resources is Pareto efficient when no
further Pareto improvements can be
made.
What is the Optimal
Amount of Externality
• 0?
• Why / Why Not? [____]
Full Cost (FC) Model
• FC = (CUT - TU) + CI + CE + CN + CA + CT
– User Costs (CU),
• Total costs borne by users (CUT).
– cost of vehicle ownership (as measured by depreciation)
– the cost of operating and maintaining the vehicle (including gas, tires,
repairs and such).
• User Transfers (TU) = (infrastructure, accident and safety)
– Infrastructure Costs (CI),
– Environmental Costs (CE),
– Noise Costs (CN),
– Accident and Safety Costs (CA), and
– Time Costs (CT).
Key Issues
• “Externalities” are Inputs to Production
System. Clean Air, Quiet, Safety,
Freeflow Time are used to produce a
trip.
• The System has boundaries: Direct
effects vs. Indirect effects
• Double Counting must be avoided
Selection of
Externalities
• Criteria: Direct Effects
• Not Internalized in Capital or Operating
Costs
• External to User (not necessarily to
system)
• Result: Noise, Air Pollution, Congestion,
Accidents
• Not: Water Pollution, Parking, Defense
...
Approach
Air
Highway Noise
Air Pollution
Congestion
Accidents
Noise: Measurement
• Noise: Unwanted Sound
• dB(A) = 10 log (P2/Pref)
• P: Pressure, Pref: queitest audible sound
• NEF: Noise Exposure Forecast is a
function of number (frequency) of
events and their loudness.
Noise: Generation
• Amount of noise generated is a function
of traffic flow, speed, types of traffic.
• Additional vehicles have non-linear
effect: e.g. 1 truck = 80 db, 2 trucks =
83 db, but sensitivity to loudness also
rises
• Noise decays with distance
Noise: Valuation
• Hedonic Models: Decline of Property
Values with Increase in Noise --> Noise
Depreciation Index (NDI).
• Average NDI from many highway and
airport studies is 0.62. For each unit
increase in dB(A), there is a 0.62%
decline in the price of a house
Noise: Integration
• Noise Cost Functions ($/pkt) : f(Quantity
of Noise, House Values, Housing
Density, Interest Rates)
• Using “reasonable” assumption, this
ranges from $0.0001/vkt - $0.0060/vkt
for highway. Best guess = $0.0045/pkt.
• For air, about the same, $0.0043/pkt.
Air Pollution:
Measurement
• Air Pollution Problems: Smog, Acid
Rain, Ozone Depletion, Global Climate
Change.
• EPA “Criteria” Pollutants: HC (a.k.a.
VOC, ROG), NOx, CO, SOx, PM10
• Other Pollutants: CO2
Air Pollution
Generation
• Comparison of Modes
Mode Pax km HC kg, CO NOx C,Ton
M kg,M kg, M M
(gm/pkt) (gm/pkt) (gm/pkt) (gm/pkt)
12
Highways 5.4 x10 5,118 32,690 5,945 263.2
(0.95) (6.053) (1.11) (46)
Jets 5.8 x1011 54 163 72.7 59.2
(0.093) (0.28) (0.13) (100)
Total 6,409 39,972 7,918
Transport
Total All 18,536 60,863 19,890
Sources
Air Pollution:
Valuation
• Local Health Effects, Material and
Vegetation Effects, Global Effects
• Greatest Uncertainty in Global Effects,
Proposed “Carbon Tax” have 2 orders
of magnitude differences
Air Pollution:
Integration
Pollutant Air Cost Highway Costs
($/pkt) ($/vkt)
PM10 --- $0.000085
SOx --- $0.000315
HC $0.0001530 $0.003850
CO $0.0000018 $0.000049
NOx $0.0001700 $0.001000
Carbon $0.0005800 $0.000260
TOTAL $0.0009048 $0.005559
Congestion:
Measurement
• Time: Congested, Uncongested
• Congested Time Increases as Flow
Approaches, Exceeds “Capacity”
• Uncongested Time: Freeflow Time +
Schedule Delay
Congestion:
Generation
• Air Transportation: Delay vs. Usage
Congestion: Valuation
• Value of Time is a function of mode,
time of day, purpose, quality of service,
trip-maker.
• Wide range, typically $50/hr air, $30/hr
car. (Business Trips more valuble than
Personal Trips).
• On other hand, average hourly PCI rate
(40 hour week) gives $10/hr
Congestion:
Integration
• Time Cost Functions:
TC = VoT Qh ( Lf/ Vf + a (Qh / Qho)b)
• highway: a=0.32, b=10
• air: a=2.33, b=6
Accidents:
Measurement
• Number of Accidents by Severity
• Multiple Databases (NASS, FARS)
• Multiple Agencies (NHTSA, NTSB), +
states and insurance agencies
• Inconsistent Classification
• Non-reporting
Accidents: Generation
• Accident Rates, Functions
• Highway: Accident Rate = f(urban/rural,
onramps, auxiliarly lanes, flow,
queueing)
• Air: Accident Rate = f( type of aircraft)
Accidents: Valuation
• Value of Life:
• average of studies $2.9 M
• average of highway studies $2.7 M
• Cost of Non-fatal accident depends on
property damage, injury (degree of
functional life lost, police costs, etc.)
Accidents: Integration
• Highway Accident Costs estimates
range from $0.002 - $0.09/pkt. Our
estimate is $0.02/pkt.
• Urban / rural tradeoff. Urban more but
less severe accidents.
• Air Accident Costs $0.0005/pkt.
Summary: $/pkt
Cost Category Air System Highway System
Noise $0.0043 $0.0045
Air Pollution $0.0009 $0.0037
Accidents $0.0005 $0.0200
Congestion $0.0017 $0.0046
TOTAL $0.0073 $0.0328
Summary: Conceptual
• High Uncertainty About Valuation
• Costs Vary with Usage
• Accounting, Difficult, but necessary to
avoid double counting.
Theoretical
Framework
• To establish optimal
emission level s for pollution,
congestion or any other
externality consider the i
TCA = c i(A i ) = c i(Z i – e i ) (2)
following framework.
is the cost of abatementwith
• Let ei = total emission from
source i. c 'A > 0 and cA 0
"
• Let Zi = amount of emission and
at source i in an uncontrolled TD = f(e) (3)
state.
is the damage function at receptorpoints
• Let Ai = Zi - ei be the
abatement at source i. (1)
• Note if Ai = 0, Zi = ei or actual
emissions equal the
maximum amount possible.
Solution
• The solution to the problem, if we consider
two sources of pollution, is to minimize the
sum of damage costs and abatement costs or
min f(e 1 + e2) + c1 (Z 1 – e1 ) + c 2 (Z2 – e2) (4)
df = dc 1 = dc 2 = c which indicates a constant marginal damage function
de dA 1 dA 2
Graphically
Optimal Amount
• The following is true: • This states that the
optimal amount of any
externality is
TCiA = c i (Z i – e i) i=1,2 established by
dc i dc i A i
minimizing the sum of
= damage and abatement
de i dA i ei
costs so we end up with
– dci = dc i E* amount of aggregate
dei dA i
pollution distributed
among the various
sources as illustrated.
Internalizing the
Externality
• If a profit maximizing firm were faced with an
abatement charge they would internalize the
externality or abate until the mc of abatement
were equal to the price of pollution or the
change; that is,
i = R(Q) – c(Q) c'(A i) –cei
c i
set =c
A i
Government Standards
• If the government wanted to establish a 'standard' it
would be . To determine these standards would
require knowledge of:
– level of marginal damages
– mc function of polluters
• It would therefore appear that there is an
informational advantage to pricing.
• The solution which has been illustrated above also
applies with:
• 1. spatially differentiated damages
• 2. non-linear damage functions
• 3. non-competitive market settings
Why Standards
Dominate Charges
• (A) Uncertainty with respect to the
marginal damage function.
• (B) Uncertainty with respect to the
marginal abatement costs.
Uncertainty with respect
to the marginal damage
function
• Now consider the situation
where the MC of abatement has
been underestimated so the
true MC of abatement lies
above the estimated MC of
abatement function. Consider a
standards scheme. Using the
estimated MC of abatement the
emission level is set at e instead
of e*. Thus, the emission level is
too low relative to the optimum.
With the level of abatement too Alternatively, suppose the authority set a sub-
high, the damages reduced due optimal emission standard of e because it is using
to having this lower level of the erroneous MD function. With emissions at e
emissions is eAce* but at the rather than e*, we again end up with a net social
cost of much higher abatement loss of ABC. Therefore, uncertainty with respect
costs of eBCe*. The net social to the marginal damage function provides NO
ADVANTAGE to either scheme; pricing or
loss will be ABC. standards.
Uncertain with respect
to marginal abatement
costs
• Now consider the situation
where the MC of abatement has
been underestimated so the
true MC of abatement lies
above the estimated MC of
abatement function. Consider a
standards scheme. Using the
estimated MC of abatement the
emission level is set at e instead
of e*. Thus, the emission level is
too low relative to the optimum.
With the level of abatement too
high, the damages reduced due
to having this lower level of
emissions is eAce* but at the
cost of much higher abatement
costs of eBCe*. The net social
loss will be ABC
Abatement: Pricing v.
Standards
• Now consider a pricing scheme. WL T = WL q = – 1 EC • e
2 1 1
D + c
2 e
The authority would set the
w here
emission charge at EC by setting
the MD function equal to the MC of WL T is the w elfare loss from pricing
abatement function. This would WL q w elfareloss from standards
result in a level of emission of e; e is e'–e
thinking this is the correct amount. D is the elasticity of the marginal damage function
But with a true MC of abatement at c is the elasticity of the marginal cost of abatement function
MCT the level of emissions which
the charge EC will generate will be The welfare loss from pricing and
e'. standards will be equal if
• e' > e* so we have too high a level 1. = in absolute value
of emissions. Pollution damages will or
increase by the amount e*CDe' but 2. ∆e = 0 or MCA = MCT
the abatement costs will be reduced
(because of higher allowed
emissions) by e*CEe'. Therefore, Standards will be preferred to charges
the net social loss will be CDE. when WLT - WLq > 0, which occurs when
• Generally, there is no reason to |eD| < |eC|. If |eC| 0 charges are
expect CDE = ABC but it has been preferred while if || 0 standards are
shown that preferred.
Rationale
• The rationale for this is:
• (a) if the MD function is steep (e.g. with very toxic pollution)
even a slight error in e will generate large damages. With
uncertainty about costs, the chances of such errors is greater
with a charging scheme.
• (b) if the MD function is flat, a charge will better approximate
marginal damages. If the damage function is linear, the optimal
result is independent of any knowledge about costs.
• (c) if the MC is steep, an ambitious standard could result in
excessive costs to abators. A charge places an upper limit on
costs.
• Therefore, the KEY in this is charges set an upper limit on costs
while standards set an upper limit on discharges.
Externalities in
Transport
• Transportation sources in North America contribute
approximately
• 47% of NOx
• 71% of CO
• 39% of HC
• To control most pollutants we have opted for standards rather
than pricing. This is reflected in the 'level of allowed emissions'
with catalytic converters on our vehicles.
• Noise is another example where the U.S. has opted for a
technological fix to achieve a standard. Europeans have,
however, introduced noise charges at some airports for aircraft
which exceed a particular noise level.
External Prices
• Externality prices can take three forms:
• 1. use to optimize social surplus
• 2. use to achieve a predetermined standard
at least cost]
• 3. use to induce compliance to a particular
standard
• Perhaps the best know 'cure' for the
congestion externality facing most major
cities has been advocated by economists;
road pricing. Standards are achieved in this
instance by continuing to build roads.
