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.
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