1 7 3
COUNTERMEASURE AGAINST EXTERNALITIES
BY THE VICTIM
Yoshiyuki Wada
This paper considers an externality_receiver called a victiln's decision_ n笠避tings about developing and nI避 〔ing use Of externality treatment technologies in a diagra― tic way. In the analysis we take into account one characteristic of externalities: whether it is possible to treat thenl aFter the overall produc― tion process is completed. It will be shO、 vn that it is unnecessary to intervene his decislon―Inakings with respect to utilizing the technologies, while it is cOnditionally justiied to regulate his behavior cOncerning the development of innovative technologies.王。 Introduction
lt goes 、vithout mentioning Coase that an externality problern involves both the generator and the receiver of it. And each agent tries to ilnprove his o、vn welfare in the situation. The ailrn of this paper is to explore the receiver's decision―makings about externality eliminating(called treatment) activities in order to decrease his damage. And in doing so, we exanline whether the victirn has an appropriate incentive to develop and utilize treatrnent technologies frOm a social point of vie、v.
I t h a s b e e n a s s e r t e d t o c l a s s i f y e x t e r n a l i t i e s O n t h e b a s i s o f s O m e criteriat benencial or harttrul, unilateral or bilateral, consumption or produc― tion, f10w Or stOck, and sO fOrth. HO、 vever there is another criteria concern― ing the tilning to treat thenl; 、vhether it is possible to treat them before or while their production process is completed as a whole. It is true that alrnost all kinds of externalities are to be treated after each unit is generated,
but it not always means that they can be treated after all of the quantity 、vhich are planned to produce are yielded. If it turns out to be impossible to treat an externality after the production process, they should be treattd before or while that process. This aspect is taken up nowhere in the literature, so we will discuss it further in terms of the victinl's behavior following Wada(1999)which dealt with the offender's behavior.
There exist several papers 、 vhich deal with an externalityttreceiver lwhat is called pollutee in environmental contexts)behavior in the literature including Oates(1983), Shibata and Winrich(1983), and Butler and MIaher (1986). They analyzed, however, the agent's static behavior in the sense that he makes decisions about how to use his existing treatrnent technologies, and they assumed the technologies to be available ex post in the above
sense. Thus, we investigate the agent's intertemporal decision― rnakings as to whether it is beneficial to develop more cost― effective technologies 、vhich are available both ex ante and ex post.
It will be shown that as for the static decislon_rllakings it is needless to regulate the externality― receiver's behavlor, while with regard to the intertemporal ones the result is ambiguous. Finally the rest of the paper is constructed as followse Section ll presents the fundamental model. In Section III we argue the receiver's behavlor concerned with innovation.
Section m/ is assigned to exanline numerical examples. Sectionヽ / consid― ers the validity of innovation in the light of the externality's characteristic, and the paper is concluded in Section VI.
Il. The Model
We make use of the same model as presented in Wada(1999).That is, there exist two agents among whom an externality conflict prevails. One of them benefits from consuming a good(ズ )in the form of β (ズ)after
COUNTERMEASURE AGAINST EXTERNALITIES BY THE VICTIPば 175
producingズ which cOnveys C(ズ )as its cost.The other agent suffers from the ttr―producing Or cOnsunling activity by this agent, whose damage is represented by D(ズ θ)whereズ θ denotes the amount Ofズ which brings about damage fOr the victiln after his treatrnent activity is finished. Let us call the first agent an O伊移γ砂溺θγ and the second one a υ ガcけを切o We assume throughout this paper that the victiln a10ne has an ability tO deve10p techno10gies tO treat the producedヌ i by the offender, which tOtally costs Tυ(ズrl whereズ けrepresents the treatedヌ by the victim.This means One impOrtant difference from the model in Wada(1999光 the determinate agents of互て's production or enliss10n level and its treatrnent level are different from each other, that is, the fOrmer is the Offender, while the latter is the victiln. The fOur functiOns have 、vell_behaved prOperties assumed in Wada(1999).
Throughout the paper we define treatrnent activities in a wide sense as any activities which prevent all kinds of damage from occurring. In this sense the treated part ofづ て give rise tO no damage tO the victiln. As we discussed treatment techno10gies avallable to the offender in Wada(1999), 、ve assume that the victirn alsO has techno10gies tO treat two types of the externality(ヌ).First,if we deal with an externality which cannot exist until its Overall production process is cOmpleted, which was called けθttο _ 陶 牲/in Wada(1999),the victim cannot help treating them before or while
the prOcess is being irnplemented. For example, people wh0 1lve near a trunk road would shut their windo、 vs in order to b10ck Off the noise brought by heavy― duty trucks while they are going through the rOad. Carrying out such a device involves cOst 、 vhich increases as the treated amount of the externality which is exactly equal to the produced and then emitted amount Of it Che number of trucks in this example)rises.
its production process is finished, 、 vhich was called pθ γsづsけθ竹ガ in Wada (1999), he can treat it both before and after the production process is completed.For instance,a lake owner can purify the lake by setting a fil― ter both at mouth of rivers by 、 vhich the lake is fed and at the bottom of the lake.The cost necessary to ilnplement such a activity is also assumed to depend only on the treated amount of the externahty irrespective of the production or ernisslon behavior on the part of the offender.
1.Treating A Temporary Type Externality
ln this subsection, we derive the socially optilnal condition to control a temporary type externality when both the offender and the victirn are present.
1.1.Socia1 0ptirnality
Keeping the assumption in Wada(1999), the socially optilnal production level of ttζ、vhich is equal to either the ernisslon or the treatment level of
it should be determined by maximizing S(ズ
)―C(ズ)―ソ
Иあ
%.{D(ヌθ
),Tυ
( ズ
リ} s u b j e c t t o ズ
= ズθ= ズけ
. T h e s o l u t i o n t o t h i s p r o b l e m i s o b t a i n e d
only if
ど' = σ' 十D ' i n t h i s c a s e ズ
テ= ズが i f D ' ( ・
) < T ド( ・
) ( l a )
Or
B'=C'十 T;in this caseズ〉=ズF if D'(。)>T。
'(。
)
(lb)is satisied. Here宏 「, stands for the socially optilnal production level of the temporary type externality.Equation(lal implles that all of theヌ produced should be emitted without treatment,whereas equation(lb)shows that the
produced ttζ is totally to be treated.
1.2.The Agents'Behavlor
ln order to induce the offender to choose the socially optirnal produc― tion level of芝て embodied in (1), it is required to regulate his behavlor by pollution control pohcies such as standards, taxes, and subsidies since it
COUNTERMEASURE AGAINST EXTERNALITIES BY THE VICTIW1 177
is apparent that the offender has no incentive tO dO sO in a laissez_faire society. Then dOes the victirn have an incentive to behave optirnally from a social viewpoint? The answer is yes. Because he endeavors to nliniFniZe the cOst he has tO incur in the circumstance, he 、 vill put up with receiv― ing damage if D(ズ テ)<Tυ (ズテ),and treat the emitted amount ofヌ if the inequality sign is Opposite.And the quantity to which the victinl is expOsed is the one the offender efficiently produced because he has nO treatinent technology.
2.Treating A Persistent Type Externality
Next we explore the socially optilnal cOndition to cOntrol a persistent type externality. In particular, we fOcus On the case that the victim utilizes treatment techno10gies after the offender's production activity is finished to contrast this with the temporary type externality case.
2 . 1 。S o c i a 1 0 p t i m a l i t y
l n t h i s c a s e , s o c i a l w e l f a r e t O m a x i m i z e i s β( ヌ) 一 C ( ズ) 一D ( ズ。) ―
T υ( ズリ s u t t e C t t o ズ= ズ θ十ズけs i n c e t h e v i c t i m h a s t h e o p t i O n t o q u a n t i ― tatively divide the enlitted amount of ttY between the one left untOuched
and the one treated due tO the feature of this typeズ . Then the necessary condition is tO silnultaneously meet the next equalities,
ズθ; 』' = σ' 十D ' a 物】 ズけ; ど' = σ' 十T ; 1 2 ) . 2.2.The Agents'BehaviOr
Assunling that the efficient prOduction of the externality is reahzed by the offender by some pollution cOntr01 policy, we have Only to inspect that the victim treats the goOd Optimally.Equation(2)implies that the efficient
t r e a t m e n t a c t i v i t y s h o u l d b e p r a c t i c e d s o a s t o s a t i s f y σ' 十D ' = c ' 十 T ;
or simply D'三 T; (2)'.
On the Other hand,the victim tries tO minimize his tOtal cOst,D(ズ° )十
the victirn encounters when he decides his treatrnent behavior. It straightforwardly follows that his optimization guarantees that(2)'is met. Thus, we have the following proposition.
P r o p o s i t i o ■1 . 丁 挽 θ υあC けづ物 あs t t θ θ? 物 ο切 れθγ げ け竹 α′γγ〃 7 砂角 θC ん物0 あり づ句 づrTespθ σけ初 θ ザ けんθ けypθ げ 渉んθ θ″″θ?ηeaιづけ銑 けんθ sοcぢaιιグ οpけづ物 aι ttγθaけ― 竹 うθ%け てア ″んθ θ冴 汐θ?竹oaJめ 汐グ ぢs γ θaιづをθ】 づ物 a ι aあssθ ″家 財あγθ θ Cο ttOI物 7.A物 】 渉んθ re9物 ιattOγ んas Ottι グ けO cο %けγOι けんθ 悌 物 】θダ Sθ ″渉θ?竹oaιぢ渉g pγ ο溺物cけづ0物
ac渉ぢυづけク.
Proposition l states that the policy by which the offender is regulated does not affect the victiln's behavior as long as the efficient production or enlls― sion of互▼ is brought about.
Ill. In■ovation and the Victim's Behatttor
lt is naturally ilnagined that the victirn develops more cost― effective treatment technologies. In this section we investigate whether he has a
proper incentive to do so and furthermore to operate those technologies. Following Wada(1999)We define technological progress or innovation in
the externality treatment methods as the do、 vnward shift of marginal treat― ment cost curve for treating a given amount of the externalityo Suppose
that innovation is taken into consideration in the deterrnination of the socially optimal production(=emission)or treatment amount of the exter… nality by the following rule.First,the victim develops a imovative technology (innovatiOn)。Next,Taking the new treatment cost function into the calcu― lation process of social welfare maxinllzation presented above leads to work― ing out the optimal values(production adiustrnent). Finally,the regulator
■ 阿 ト ト ー ト ー ー ー ー ー ー ー ー
COUNTERMEASURE AGAINST EXTERNALITIES BY THE VICTIい 江 179 values(cOntr01 adjustmentl)In the situatiOn in this paper,however,we
focus On the victiln's behav10r assurning that the offender always brings about the efficient production and enlisslon amOunts Of挑ュ Thus, it is the only cOncern fOr us 、vhether the victiln has an incentive to develop and ilnplement cost_effective treatrnent technologies.
1.Innovation in Techno10gies tO Treat A TernpOrary Type Externality Let us sttt ngure l whch mustrates the ophmtt dtuadOn embOdied by equation(1). In this figureズ * denotes the socially optilnal prOduction leve1 0fづて in the absence Of treatrnent techno10gies. With the less cOst… effective techno10gy whOse marginal cOst is given as T;',the efficient
production level is Obtained asズ
テ
1.If the more cost―
effective techno10gy
is developed which is represented by T塚
'as its marginal cOst,the level is
modified toズ
あacting on equality(lb).In these circumstances does the
victiln have a prOper incentive to develop innovative technologies and tO implement them?Were it not fOr production adjustment,that is,if the
enlitted amount Of立てby the ottender is unchanged at互 て*、vhether the victim develops a treatrnent technology or not, he would be willing tO develop and irnplement them. In Other wOrds, he surely operates it because he incurs damage of Oaん if avOiding utilizing the technology, 、vhile he bears O】ん if he carries out it. Evidently Ooん is larger than O】ん by Oaが , sO he would ch00se tO treat the externality, Ho、 vever, there exists production adiustment.TherefOre,the realized emiss10n Ofズ isズ 品 instead ofズ 米 after he generates a technology, and he has tO incur Obづ in its Operation. Consequently the victirn will treat the externality if Oa】 ;>】んぁb. In this inequality the left…hand side shOws the cost reduction due to treatrnent
1 ) T h e t e r m s i n t h e p a r e n t h e s e s Wada(1999).
2)Procedures to derive Figures l
are quoted from tt1111lIIlan and 2 are brieay explained
and Prince(1989)and in ヽVada(1999).
technology development, while the right― hand side is the cost increase because of the rise in enlission ofス
By the same reason the victirn will operate the more cost―effective technology instead of the less cost―effective one if Obθ,>θゥ竹 sinCe pro― duction adiuStment makes the production or emission amount ofズ which leads to the victimズル.
2. Innovation in Technologies to Treat A Persistent Type Externahty ln Figure 2 we demonstrate the optilnal production, enllssion, and treatment of a persistent type externality. Supposing that the victirn whose techndogy entails T;'as is margin】 cost caHes out hs treatment act持 ―
i t y e x p o s t , t h e o f f e n d e r s h o u l d p r o d u c e ズ
u p t o ズ
ど
l i n w h i C h ズ
マ
求i s l e f t
alone by the victim andズ
Ftt be treated by him.If he develops a more costぃ
effect市
e techndogy whch tt accompatted by T▼
'as tts mar」
n】COSt,on
the other hand,the offender shodd produce恢
ど
2 h WhChズダ為rece市
ed
as it is by the victim and he treats Xダ
.These are diagrammatic appli―
cation of equation(2). As in the case of a temporary type externality, the victiln would voluntarily try to develop a more efficient technology in the absence of production adiustment. However, the fact that his innovative technologies are reflected in the process of production adiustrnent in the form of an increase in the amount ofサ て Inight have the victirn hesitate to do so.If it were not for treatment technologies,he would bear Oげ aS dam_ age since the offender produces and enlits O率Ⅲ. If the victiln has a treat― ment techndogy which mar」 n】け COStS T∴ he has to sustain O物 as the sum of damage and treatment cost. Thus, he will treat the externahty if
ab溺 >匂 り。Sirnilarly he will rnake use of the more efficient technology
given by T♂
'as tts marginal cost r bcθ
>りんin which theに
■―
hand dde
denotes cost reduction due to innovation and the right―hand side means
COUNTERh/1EASURE AGAINST EXTERNALITIES BY THE VICTIMl 181 mente Consequently we have the subsequent proposition.
Propositiom 2.r//2 渉 ん θ pγ θsθ %cθ りr pγ ο】 物 CけづOtt aり 物 sけ?物 θ物 け けんθ υぢcけづ物 切 づ況 けタフ 汐θ ttθ υθιop a物 溺 物 αんθ ttsθ げ づ物 物 ουa汐 あυθ け?セ a′ ンγみθ%汐 汐θcん 物 OιOθ づθs ゲ けん θ ?んθS物 筋づ竹 θ σ οsけ γθ】物 cむぢ0物 づs ι attθ θγ けん a物 けんθ cosけ づ物 cγ θasθ 】物 θ けο
れθ aり をしS汐物θ物け.
In the next section we give a tentative evaluation of the above situation by means of numerical examples.
IV. Numerical Examples
ln order to obtain a concrete result, we employ the following examples of the above functions:
B岡=路
―
竹一
つ
2にズ≦
っ
,C∽
=干,
D側=ノ,Tl留
)=ず,T♂
留)=ギ
1.The Ternporary Type Externality
Suppose first thatズ is a temporary type externality. Then following the optirnization condition(1)leads to the socially optirnal value of each
vanabに
r(ガ ,ズれ,ズ品)=(16/9,16/7,8/3).Making use of these v】
ues,
、ve can conclude that
D(ズ *)≧3.16>T‖ (ズテ1)≧ 2.61>T?(ズ あ)≧ 1.78 14). This shows that the victirn has an adequate incentive to develop and utilize cost―effective treatrllent technologies since the cost reduction exceeds the treatment cost increase.
2.The Persistent Type Externality
ericttnt values of the vanables turn out to be as follows;任
お
1,ズ
r来
,ズF*)
=(48/19,16/19,32/19)andは
お
2,ズ
塚
氷
,ズダ)=(80/29,16/29,64/29)
by equation(2).It follows from these results
D ( ズ求) ≧3 . 1 6 > D ( ズ ダ) 十 T 〕( ズF ) ≧ 2 . 1 3 > D ( ズ ダ ) 十 T ? ( ヌダ) ≧ 1 . 5 2 ( 5 ) . It is concluded again fronl inequality (5)that in these circumstances the victim will try to benefit from treatment activities.
V. Validity of IRI10Vation in the Light Of the Nature of Extermalities
Does innovation in treatment technologies always contribute to irnprov― ing the victirn's as well as social welfare?Dealing with a temporary type externality,if we observe that D'<Tマ '<Tl',the victim would restrain from employing both the existing and more efficient technologies since putting up 、vith damage costs hirn least. Therefore, to put innovation to practical use, the condition
Tマ
'<〃
れ.{D',Tl'}
needs to be satisfied. As for the technologies to treat a persistent type externality, if it is treated ex ante in the sense that the treatment activity precedes the completion of production Ofヴ て, the conclusion is the same as in the case of the temporary type. If the externahty is treated afteF the production process is finished, on the other hand, the situation changes. For only if T♂'<Tl'holds,the victim would have an incentive to use
3 ) the more cost― effective technology in order to nlinilnize his overall cost. Because the victiln's optilnization coincides 、 vith social welfare, the above conclusion can also be verified froHl the social viewpoint. Therefore, we have
3)This assertion is valid on condition that the effect of production adjustment is negligible,
COUNTERMEASURE AGAINST EXTERNALITIES BY THE VICTIい に 183 Proposition 3.五 れ物ουa渉ぢοtt aιttaグs cο物けγぢb物 汐θs ttο ぢ%cγ θasぢ物g sο cぢaι
物θゲaγθ づ物 けんθ casθ げ け
んθ
θ″ pοsけ
ぢ物pιθttθ
物け
aけ
を
0物 げ け
γ
θaけ
?物
θ物け
渉θcん 物 οιοgあθs ttγ a pθ γsづsけθ物 け けグpθ θ ″渉θ?竹eaιぢ渉銑 切 んづιθ づ物 けんθ casθ s cァ うな θ″ a物 けθ ぢ竹 pιθttθ 物 汐aけあOtt attd aけ θttpο γaγ υ けグpθ θ 冴渉θ?竹oaιづけグ けγθaけ?物θ物 け づけ あs?4θ ?功 ぢγθ冴 けο ttθ θけ を物θ?物 aιあけり 6の けο υ aιづ冴attθ あ物物ουaけづυθ α ttCけS.
Ⅵ. Concluding Remarks
We have investigated an externahty victiln's decision― IIlakings 、vith respect tO his externahty treatment activity and attempt to develop innOvative treatrnent technologies in connection with the characteristic of the exter_ nality: temporary type and persistent type. In the process 、 ve have obtained the following results. First, if the victiln is the only Owner of treatrnent technologies the regulator exclusively needs to inspect the offender's prOduc― tion behavlor since the victiln has an adequate incentive tO irnplement his treatment efficiently.Secondly,faced with production attustment and the resulting cOntrol adiuStrnent, the victirn adopts innovative technologies if the cost reduction exceeds the treatrnent cost increase.Third, there exists absolute reliability for innovation to be effective in irnproving social 、velfare only in the case of ex post treatment of a persistent type externality.
It is widely recognized in the literature that it is desirable not tO intervene a victiln's behavlor to achieve sOcial optirnality with regard tO pollutiOn control. Ho、vever, there is no distinct explanatiOn that his innova― tion behavlor should also be kept being untOuched tO accomplish the eri… cient situation. In this sense 、 ve have made clear the condition under which a laissez― faire p01icy to、vards the victirn is vahd in the shOrt run as 、vell as in the long run.
We have not taken up a situation in which bOth Offender and victiln have treatrnent technologies bet、 veen 、vhich there is a technical relation_
ship affecting each technology's performance. In these circumstances, are the results in this paper still accurate? It seems that the need for controll― ing the victirn's behavlor is also brOught about since there exists another externality bet、 veen the agents' technologies which nlight be ineffi― cient in a laissez…faire regilne.
σ'十Tダ
ヌ氷 ズ が1 FIGURE
ズ米写 1 対 2
COUNTERMEASURE AGAINST EXTERNALITIES BY THE VICTIM 185 References
Butier,R.V.and M.Do Maher(1986),“ The Control of Externalitiesi Abatement vs.
Damage Prevention",Sο 切けんθ竹れ 『 cοttθ物 あc」 θ物?竹をaら V01.52,pp.1089-1102.
M I i l l i r n a n , S . R , a n d R . P r i n c e ( 1 9 8 9 ) , “F i r m l n c e n t i v e t o P r o m o t e T e c h n o l o g i c a l C h a n g e
in Pollution Control",」 b切 ?物 aι cア β%υ ぢγο物竹みθ物けaι ECθ %θ 竹砂'CS a物 冴 虹 Q%99θ 物 好物ち V01・
17, pp,247,265.
Oates,W.E。 (1983),“The Regulation of Externalitiesi Etticient Behavior by Sources and Victilns",PttbιづcFづ 物attca vol。38,pp.362-375,
Shibata,H.and」 . S,Winrich(1983), “Contr01 of Pollution When the olended Dettnded Themselves'',Ecοttο物づCぅ V01.50, pp.425-437.
Wada,Y。 (1999),“TreatIIlent Technologies and Pollution Contr01 in the Light Of lts Nature",質 んθム物物aιsげ Fr1/物αtt a%α Sοc,aι Scぢθttca V01.6,pp.69-81.
