Envionmental Extenalities in the Pesence of Netwok Effects: Adoption of Low Emission Technologies in the Automobile Maket Eftichios S. Satzetakis 1 Depatment of Accounting and Finance, Univesity of Macedonia 156 Egnatia St., Thessaloniki 54006, Geece Panagiotis Tsigais Depatment of Economics, Thompson Rives Univesity Box 3010, 900 McGill Road, Kamloops, BC., Canada V2C 5N3 ABSTRACT: The pape consides a maket cuently dominated by a dity technology that imposes significant envionmental costs. A clean technology, with zeo envionmental costs, is intoduced afte the matuity of the dity technology's netwok. Adoption of the clean technology is not possible due to the netwok benefits in favou of the dity technology. The pape consides two types of policy intevention to coect fo the envionmental extenality. Fist, we find that the tax necessay to induce adoption of the clean technology is vey high implying that a tax equal to the maginal envionmental damage would not esolve the extenality poblem in many cases. Second, if tax evenues ae eamaked towads subsidizing the clean technology, the tax is lowe than in the pevious case and can be set equal to the maginal extenal damage. KEYWORDS: Envionmental extenalities, netwok effects, automobile maket, fuel cell tegnology. 1 Coesponding autho: Eftichios S. Satzetakis, Depatment of Accounting and Finance, Univesity of Macedonia, 156 Egnatia St., Thessaloniki 54006, Geece. Email addess: esatz@uom.g. The authos would like to thank Robet Andokovich, Jim Seldon, Godon Tazwell, Chistos Constantatos and paticipants of the Sevilla Wokshop on Public Economics and the Envionment 2004 fo thei suggestions. Financial suppot by the Scholaly Activity Committee of the Thompson Rives Univesity is acknowledged by both authos. Eftichios Satzetakis acknowledges also financial suppot by the Pythagoas I eseach gand of the Geek govenment.
1 Intoduction The tanspotation secto contibutes significantly to both local and global ai pollution. At the local level, mobile-souce pollutants ae esponsible fo a significant pat of the main elements of uban ai pollution, namely, cabon monoxide (CO), nitogen oxides (NO x ) volatile oganic compounds (VOSCs) and paticulate matte (PM). 1 At the global level, mobile-souce pollutants ae esponsible fo a substantial pat of the anthopogenic eleases of cabon dioxide (CO 2 ), the most impotant of the geenhouse gases esponsible fo global waming. 2 Most of the existing policies tageting automotive ai pollution focus on the low level pollutants which affect local ai quality. In the U.S.A. these policies date back to the fifties fo the state of Califonia, and the Moto Vehicle Ai Pollution Act of 1965 at the fedeal level. 3 Simila policies have been adopted in most industialized nations. The success of these policies elies on the fact that it is technically possible to educe low level pollutants without eplacing the conventional intenal combustion engine. 4 Howeve, this is not the case fo CO 2 emissions. Inceases in fuel efficiency could educe CO 2 emissions. Howeve this eduction has been poven to be insufficient to offset the eve expanding use of automobiles. 5 In geneal, thee ae two policy appoaches that could addess the poblem of automobile emissions. The fist appoach addesses the need to educe diving by poviding pice incentives in the fom of gasoline taxation. Gasoline taxation has been seiously consideed ove the last decade, usually as pat of a boade package of cabon/enegy taxes. Gasoline taxation has aleady been applied in a numbe of counties with consistently minimal esults due, in pat, to the inelastic natue of the demand. 6 The second appoach is to pomote the adoption of a totally new 1 Accoding to the Envionmental Potection Agency (EPA), in 1996 automobiles accounted fo oughly 60% of total emissions of CO, 31% of NO x, 30% of VOCs and 8% of PM. See EPA (1998) and in paticula pp. 82-86. 2 It has been estimated that moto vehicles contibute somewhee between one fifth to one thid of total CO 2 emissions depending on the county. In the EU, fo example, the tanspotation secto accounted fo 28% of CO 2 emissions in 1998, as epoted in Euopean Envionmental Agency (2000). 3 Tietenbeg (1996) povides a eview of the histoy and the stuctue of egulatoy intevention in Chapte 17. 4 If an engine is unning efficiently, the poducts of combustion ae mainly cabon dioxide (CO 2 ) and wate. Emissions of othe pollutants is the esult of low speed and idling engines that yield incompletecombustion,aswellasofimpuitiesinthefuelssuchasnitogen. 5 Fo example, in the EU, tanspotation is the only secto whose emission shae has inceased. The emission shae inceased by 3.1% ove the peiod 1990-98. This is due to the inceased taffic, which gew by 14.7 % duing the same peiod. See section 3.3. of the Euopean Envionmental Agency (2000). 6 Both shot and long un demand fo fuel has been found to be inelastic, with the shot un elasticity being lowe. P. Goodwin, J. Dagay and M. Hanly (2004) eview a numbe of ecent empiical studies that povide data on the effects of pice changes on fuel consumption, taffic levels, 1
type of vehicle that does not use fossil fuels, and theefoe does not contibute to eithe local o global pollution. Fo example, fuel cells in which hydogen eacts with oxygen to poduce electicity do not geneate emissions. Although fuel cell vehicles ae cuently tested on the oad, they ae still not an economically viable altenative to conventional vehicles. 7 Fuel cell vehicles have to ovecome obstacles such as the elative pice diffeential, the baie that consumes ae completely unfamilia with the technology, and the nonexistence of geneation, distibution, sevice, and efueling netwoks. Thee ae two options in developing this type of clean technology s netwok. Hydogen will eithe utilize the existing gasoline infastuctue o a totally new hydogen infastuctue will be developed. The second option equies a new geneation and distibution system as well as the convesion of existing efueling stations to stoe hydogen. The degee of netwok compatibility is both a technical and an economic issue. 8 All existing studies estimate high costs fo both options, which implies a low degee of compatibility. 9 To simplify the analysis we assume that the two netwoks ae incompatible and that a new geneation and distibution system is equied to supply hydogen. Thus, upon thei intoduction to the maket, fuel cell vehicles will face a significant handicap elated to netwok extenalities. 10 Netwok effects exist when the utility consumes deive fom the use of a good o sevice depends upon the numbe of uses aleady using the same good o sevice. Automobiles ae subject to netwok effects since the utility that consumes deive fom the use of thei vehicle is positively elated to the sevices they can enjoy, which in tun ae positively elated to the numbe of consumes aleady using automobiles. Conventional technology vehicles dominated tanspotation only afte the establishment of a netwok of gasoline stations, epai shops, paved oads, etc. 11 Although pat of this netwok, such as oads, could be utilized by fuel cell vehicles, thee ae substantial netwok effects that ae technology specific. fuel efficiency and ca owneship. See also the OECD (1997) study on taxation as an instument to educe fuel consumption. 7 Othe altenatives include the electic and hybid electic vehicles. 8 It has been suggested that the netwoks incompatibility would be avoided by using a efome that extacts hydogen fom gasoline, thus, making the two systems (backwad) compatible (See Unuh (2002)). Howeve, the Depatment of Enegy (1999) study on the development of hydogen infastuctue indicates that building a new netwok, although it equies geate up font investment, povides a bette system-wide pefomance. 9 Fo example, D Angelo and Bilalis (2004) estimate the cost of conveting just 10% of the 135,000 filling stations in the EU to hydogen use, at 10-12 billion euos. 10 Liebowitz and Magolis (1998a) have expessed thei concen ove the use of the tem "netwok extenalities", especially if the maket paticipants have intenalized these effects. They suggest using the tem "netwok effects". In the est of the pape we adopt this teminology. 11 The undelying easons behind the pevalence of the intenal combustion ove steam engined and electic vehicles duing the late 1800s and ealy 1900s ae discussed in Foay (1997), Foeman-Peck (1996) and Kisch (2000). 2
In addition to the diect netwok effects on use s utility, thee ae also pice effects. As the size of the netwok inceases, both the pice of the automobile and the sevice chage deceases due to the usual leaning cuve effects on poduction as well as the pesence of economies of scale in the poduction and distibution of spae pats and fuel. Thus, the technology with the lage netwok also has a pice advantage. Both utility and pice netwok effects favou the incumbent dity technology. Howeve, if the extenal costs associated with the emissions of the dity technology exceed the pivate net benefits, thee is a need fo policy intevention to suppot the adoption of the clean technology. Despite the fact that the significance of netwok effects in the automotive maket has been ecognized in the liteatue, to the best of ou knowledge thee is no wok addessing the issue of envionmental policy in the pesence of such effects. This pape is a fistattempttofill this gap. We develop a simple model of the automobile maket in which significant netwok effects ae pesent and which is cuently dominated by a technology that geneates an envionmental extenality in the fom of emissions. Assuming that at some point in time an altenative zeo-emission technology becomes available and that its adoption would be socially optimal, we addess the following two questions. Fist, will the system exit the lock-in on its own and adopt the clean technology? 12 We find that, in the absence of policy intevention, the benefits of the installed base and the pice diffeentials in favou of the existing technology will dete new uses fom adopting the clean technology even if the envionmental gains exceed the pivate losses. 13 Second, if pivate incentives ae not sufficient to induce the desied technological tansition, what fom should public intevention take? We conside two altenative policies in pomoting the adoption of the clean technology. We fist conside a tax on the dity technology assuming that the tax evenues ae used to finance the govenment s geneal budget. We find that the tax necessay to induce adoption of the clean technology is vey high in ode to offset the installed base benefits and pice diffeentials in favou of the dity technology. Howeve, we also find that adoption of the clean technology can be socially desiable even when maginal envionmental damages ae lowe than the equied tax needed to induce 12 Ou analysis is based on the pemise that in the absence of envionmental extenalities the cuent technology is efficient. Thee is no maket failue due to netwok effects, since both technologies shae the same chaacteistics. The only maket failue is due to the envionmental damages of the dity technology. 13 This esult is suppoted by the data on maket penetation by altenative technology vehicles. Although in the last few yeas thee has been an incease in the amount of altenative fuel vehicles (AFVs) due to govenment policy estictions (i.e., see the 2003 Amendments to the Califonia ZEV Regulation), the estimated numbe of AFVs on the oad and gasoline/diesel-electic Hybid Vehicles fo 2001 is at 623,043. This epesents a maket penetation of only 0.26 pecent (See Altenative Fuel Vehicles at the U.S. Enegy Infomation Administation, accessible at www.eia.doe.gov and the Bueau of Tanspotation Statistics at ww.bts.gov fo total numbe of vehicles in U.S. maket). Cowan and Hulten (1996) also each simila conclusions. 3
adoption. In essence, a tax equal to the maginal envionmental damage would not esolve the extenality poblem in many cases. Second, we conside a combined policy instuments egime in which the govenment commits to use the evenues fom a tax on the dity technology to subsidize the clean technology, unde a balanced budget constaint. We find that the tax-subsidy combination necessay to induce adoption of the clean technology involves a tax that is lowe than in the pevious case. Thus, unde the combined policy instuments egime it is moe likely that a tax equal to maginal envionmental damage could induce adoption of the clean technology. The pape builds upon the liteatue on netwok effects. In a seies of papes, Bian Athu examined the choice of technology in the pesence of netwok effects. Athu (1989) showed how small accidental histoical events can lock an economic system into an infeio technology due to the pesence of netwok effects, lock-in and path dependency. Athu (1988) suveyed dynamic systems of the self-einfocing type that exists in many aeas of economics. Liebowitz and Magolis, in a seies of aticles (1990, 1995a,b, 1998a,b), have agued that the pesence of netwok effects and path dependency does not necessaily imply that maket outcomes ae inefficient. They poceed to popose thee classes of path dependence. Fist-degee path dependence efes to the class of systems that ae sensitive to initial conditions. Second-degee path dependence efes to the class of systems whee the sensitivity of initial conditions leads to an infeio outcome. Howeve, the infeioity of the outcome appeas ex post. Lastly, thid-degee path dependence efes to the class of systems whee the sensitivity of initial conditions leads to an infeio outcome that is emediable. Thus, small accidental histoical events alone do not imply that the outcome is inefficient. The class of systems that have sensitivity to initial conditions and ae infeio ex post cannot be labelled infeio at the time of the choice since the state of knowledge is impefect. Liebowitz and Magolis (1995a) stated that the thid-degee path dependence, although it implies emediable inefficiency, is ae and if it occued would be wothwhile analyzing. Foay (1997) agued that emediable lock-in is a self contadictoy poposition since it would equie the elimination of technological uncetainty. Katz and Shapio (1986a) examined the effects of netwok effects on technology adoption, while Katz and Shapio (1985) and (1986b) analyzed the pivate and social incentives to achieve technical compatibility. Faell and Salone (1985) studied fims incentives to exit fom a lock-in when neithe technology is popietay. They found that the esult depends on whethe fims have complete infomation egading othe fims actions. Faell and Salone (1986) showed that a new technology may not be adopted when the existing technology has aleady built a stong netwok. The benefits of the existing technology s installed base can esult in a bias against supeio technologies yielding excess inetia. Ou analysis is closely elated to the appoach developed in Faell and Salone (1986). Ou model is based on excess inetia and 4
envionmental extenalities. 14 The pape is oganized as follows. In section 2 we pesent the model emphasizing the elements of individual decision making. In section 3 we examine the technology choice of individuals without taking into account envionmental extenalities. In section 4 we take into consideation the fact that the existing technology imposes envionmental damages and we examine the effectiveness of envionmental policy. The last section concludes the pape. 2 The model Assume that thee ae two types of technology in the automobile industy: the cuently available, denoted by D (dity), and the new technology denoted by C (clean), whichisintoducedatsometimet > 0. Weassumethatthenetwoksofthetwo technologies ae incompatible. Uses aive at the maket continuously ove time with aival ate n(t) and they have inelastic demand fo a single automobile. Fo simplicity we futhe assume that each consume is infinitely-lived and that the poduct is also infinitely duable, so that uses do not ente the automobile maket at any othe point in the futue. Theefoe we ignoe the possibility of switching technologies. 15 At time t, N usesaeinthemaketwithn(t) = R t n(s)ds. Weassumethesimplest 0 fom of maket gowth, a linea gowth with just one use aiving at the maket pe peiod of time, that is, n(t) =1and hence N(t) =t. As the numbe of uses of a given technology inceases, so does the numbe of sevice stations fo this paticula technology. To avoid adding unnecessay notation, we assume that one sevice station opens up with evey new use of the coesponding technology. Basically the size of the netwok gows as follows x(t) =N(t) =t. We assume that automobile uses eceive benefits that ae inceasing in the netwok s size up to the matuity of the technology. Afte the netwok s matuity, uses netwok benefits ae constant. 16 Pio to the matuity of the technology, each use that puchases the dity [clean] technology enjoys a flow of benefits D(x(t)), [C(x(t))] at time t, at which the netwok size is x(t). Fo simplicity, we assume linea netwok benefits, that is, benefits at time t ae a + bx(t), wheea denotes the benefits in- 14 In Faell and Salone (1986) "excess inetia" was an exceptional case and envionmental extenalities wee not pesent. 15 Existing uses have paid fo the D-technology and assuming that the pice of the clean technology is high enough, it will peclude these D-uses switching to the new clean technology. This is a simplifying assumption that does not affect the conclusions of the model but affects the maket size at any paticula point in time. 16 This assumption, that the netwok benefits each a maximum, eliminates one of the poblems of netwok models pesented by Liebowitz and Magolis (1998a). Liebowitz and Magolis agued that one of the diving foces behind the outcomes of netwok models is the assumption of linealy inceasing, unbounded benefits. 5
dependent of the netwok s size, and b measues the stength of the netwok effect. Given that x(t) =N(t) =t, totalbenefits at time t ae a + bt. Uses pay a puchasing pice and a pice fo sevicing thei automobile, which includes the pice of the fuel that each technology uses as well as the pice fo sevicing the automobile. 17 The sevice pice of the automobile, inclusive of the puchase pice, deceases as the size of sevice stations netwok stengthens, because of the usual leaning cuve as well as the pesence of economies of scale in the poduction and distibution of spae pats and fuel. The sevice pice deceases up to the time that the netwok matues. The sevice pice the use has to pay at time t is a deceasing function of the netwok size, that is, p D0 (1 zx(t)), wheep D0 is the pice at the time that the dity technology is intoduced and z is a positive paamete denoting the sensitivity of pice to the netwok s size. The assumption x(t) =t, yields, p D0 (1 zt). The pesent value of the flow of net benefits up to time of netwok s matuity T 1 to a use that puchases the dity technology at time T<T 1,is R T 1 (a + bt p T D 0 (1 zt)) e (t T ) dt, whee denotes the constant discount ate. Afte the netwok s matuity and egadless of whethe the netwok of the dity technology keeps gowing o not, each use eceives a constant flow of benefits a + bt 1 and pays a constant sevice pice pe peiod p D1 = p D0 (1 zt 1 ) > 0, which is the lowest sevice pice possible. Thus, the value of the flow of benefits fomh time T 1 up to infinity, evaluated at time R i T at which the use entes the maket, is T 1 (a + bt 1 p D1 ) e (t T1) dt e (T 1 T ). Theefoe, the pesent value of the net benefits the use, enteing the maket at time T, gets is: D(T )= Z T1 T [a + bt p D0 (1 zt)] e (t T ) dt +(a + bt 1 p D1 ) Z T 1 e (t T ) dt = a + bt p D 0 (1 zt) + b + p D 0 z 1 e (T 1 T ). (1) 2 The use adopting the dity technology at time T, joins a netwok of size T and so the benefits in that peiod ae a+bt, while the use pays a sevice pice p D0 (1 zt). The fist tem in equation (1) gives the discounted sum of the steam of net benefits fom T to infinity, if the netwok does not gow any futhe, denoted by ed(t ). Ifthe netwok continues to gow afte T, ataateofb, the use eceives additional benefits b fom the use of the automobile, and benefits p D 0 z fom the sevice pice eduction evey peiod. Since the netwok ceases to gow afte time T 1, the discounted value of these benefits is b+p D 0 z 1 e (T 1 T ),whichisthesecondteminequation(1). 2 Thus, fo any use enteing the maket afte the matuity of the dity technology s netwok (i.e., T>T 1 )wegetthatd(t 1 )= D(T e 1 ). 17 The puchase pice can be consideed pat of the sevice pice without a loss of geneality. 6
The clean technology uses benefits ae definedinasimilaway. Tofocuson the envionmental policy issue, we assume that both technologies shae the same chaacteistics, that is, a, b, p C0 = p D0,andz, ae the espective paametes unde the clean technology. We assume that the netwok of sevice stations suppoting the clean technology eaches matuity at time T 2. 18 If all new uses aiving at the maket afte time T adopt the clean technology, the pesent value of net benefits to the use enteing the maket at time T is: C(T )= Z T2 T [a + b (t T ) p C0 [1 z (t T )]] e (t T ) dt +[a + b (T 2 T ) p C1 ] Z T 2 e (t T ) dt + (b + p C 0 z) 2 1 e (T 2 T ). (2) = a + b (T T ) p C0 [1 z (T T )] The intepetation of equation (2) is simila to that given fo equation (1). If the use who adopts the clean technology at time T isthelastuseofthenewtechnology, the pesent value of the flow of he net benefits is, e C(T )= a+b(t T ) p C0 [1 z(t T )]. Thus, if the use entes the maket afte the matuity of the new technology s netwok (i.e., T>T 2 >T ) then C(T 2 )= ec(t 2 ). 3 Nash equilibium adoption decisions by uses A use aiving at the maket befoe the intoduction of the new technology, that is, at time t<t, does not have any choice but to adopt the dity technology. We assume that all uses enteing any time befoe T choose to puchase, that is, we assume that a>p D0. A use that entes the maket afte the intoduction of the clean technology, that is, at time t T, chooses between the dity and the clean technology automobile, given the decision of all pevious uses. The Nash equilibium is chaacteized by the netwok effect which has been temed in the liteatue eithe as the bandwagon o installed-base effect. Simply put, the moe uses continue to adopt the dity technology afte the intoduction of the clean technology, the moe difficult it becomes fo the latte to eve be adopted. We examine the equilibium decision of uses afte the intoduction of the new technology. Two possible outcomes aeconsideed:adoption,thatisthecasewheeallusesadoptthecleantechnology afte its intoduction, and non-adoption, the case whee no use adopts the clean technology. 18 Fo simplicity we assume that the equied time fo matuity is the same fo both netwoks, that is, T 2 T = T 1. 7
Adoption is a subgame-pefect Nash equilibium if the use enteing the maket at time T puchases the clean technology automobile. This occus if the use s discounted futue benefits fom C, assuming the netwok of clean technology keeps expanding, exceed those fom D, assuming that the netwok of the dity technology ceases to expand, that is, C(T ) D(T e ). If the use at T finds it beneficial to adopt the clean technology, it is cetain that all subsequent uses will do the same. 19 Adoption is the subgame-pefect Nash equilibium. Adoption is a unique equilibium if ec(t ) > D(T ), that is, if the net pesent value of the benefits fom the clean technology to the use enteing at time T ae highe even if she is the only use of the clean technology. If instead, D(T ) ec(t ),thenalluseswillkeeppuchasingthe dity technology. In this case, non-adoption is the subgame-pefect Nash equilibium. Non-adoption is a unique equilibium if ed(t ) > C(T ). Poposition 1 summaizes the esults in the case that no envionmental concens ae aised. The poof of Poposition 1 is delineated in the appendix. Poposition 1 Assuming the clean technology is intoduced afte the matuity of the dity technology s netwok, the existence of netwok effects and/o the pice diffeential in favo of the incumbent technology, endes the intoduction of the clean technology impossible. Non-adoption is a unique equilibium and it is also efficient. Figue 1 illustates the net benefits of the two technologies. The cuve ed ( ec) pesents the net pesent value of benefits a use enjoys if she is the last puchasing the dity (clean) technology. These benefits ae inceasing ove time at a constant ate of b + z. If the netwok continuous to gow, the net pesent value of benefits is pesented by the D and C cuves whose slope is inceasing in a deceasing ate, i.e. D/ T > 0, C/ T > 0 and 2 D/ T 2 < 0, 2 C/ T 2 < 0, T, T [0,T 1 ).Sincewe have assumed that the two technologies shae the same chaacteistics and T >T 1, non-adoption is a unique equilibium as shown in figue 1. In the case of an ealy intoduction of the clean technology, that is, T <T 1, thee could be multiple equilibia since pat of the C cuve could lie above the ed cuve. Altenatively, adoption could be the equilibium if the new technology was intoduced ealy and offeed eithe supeio netwok-independent o netwok elated benefits. In this pape we focus on the wost possible case fo adoption of the clean technology, namely the case in which the netwok of the dity technology matues befoe the intoduction of the clean technology. 19 Becauseusesaeinfinitesimal, any deviation by a single use will not affect the choice of subsequent uses. See Faell and Salone (1985). 8
Benefits (a-p D0 )/+ (b+zp D0 )T 1 / ~ D = D (a-p D0 )/ +(b+zp D0 ) (1-e -T1 )/ 2 (a-p D0 )/ D ~ D C ~ C T 1 T * T 2 t Figue 1: Pivate benefits deived fom the dity and the clean technology 4 Envionmental extenality and public policy Assume now that the use of dity technology automobiles imposes envionmental damages on society. We assume that the envionmental damage, ε, that each use geneates is constant pe peiod of time and the same fo all uses. Theefoe, the total envionmental damage that a use enteing the maket at time T imposes upon the society is, Z T εe (t T ) dt. (3) Sinceweassumethatallusespuchaseanautomobile(fullmaketcoveage),and futhe that thee is no vaiation in the diving activity among uses, the pe peiod envionmental damage is the same fo all uses. Fo simplicity we assume that the clean technology automobile has zeo envionmental impact. Thus, the pivate benefits of the C technology equal the social benefits. Fom the pevious section we know that D(T ) > C(T ), T 2 >T >T and D(T 1 )=C(T 2 ), T>T 2. Fo uses aiving at time t [T,T 2 ] and puchasing the 9
Benefits (a-p D0 )/+ (b+zp D0 )T 1 / ~ D = D ε/ ~ C = C C (a-p C0 )/ +(b+zp C0 ) (1-e -T1 )/ 2 ~ C (a-p C0 )/ T 1 T * T 2 t Figue 2: Welfae effects of the adoption of clean technology clean technology, the policy make has to compae thei pivate loss, D(t) C(t), to the social benefits esulting fom the educed envionmental damage. Figue 2 illustates the situation. The vetically shaded aea epesents the educed pivate benefits fo all uses aiving duing the time peiod t [T,T 2 ], if the clean technology is adopted at time T. The hoizontally shaded aea epesents the envionmental damage that all uses enteing the maket afte time T wouldimposeonthesociety if they adopt the dity technology. Since the losses in pivate benefits fom the adoption of the clean technology shink as the installed base of the new technology inceases, thee could exist a lage enough value of ε that could make adoption of the new technology, at the time of its intoduction, welfae supeio. Howeve, fom the pevious section we know that the clean technology will neve be adopted based on pivate incentives. Theefoe, policy intevention is waanted unde the following condition, Z T2 W T = C (t) D (t) e (t T ) ε dt + T T e (t T ) dt > 0. (4) In what follows, we assume that the above condition holds and we conside the 10 Z
effectiveness of envionmental policy intevention. 4.1 Tax policy We examine fist the case in which the govenment decides to impose a tax τ on the dity technology. The tax is imposed on the sevice pice of the dity technology and paid each peiod of time. We assume that the govenment imposes the tax effective at some peiod T τ,wheet 1 <T τ T. Poposition 2 pesents the level of tax sufficient to induce adoption of the clean technology as the Nash equilibia. Poposition 2 The level of tax sufficient to induce adoption of the clean technology as the Nash equilibia is τ m =(b + zp D0 )T 1. Poof. In ode to induce new uses to adopt the clean technology, the tax has to be such that adoption becomes a unique equilibium, that is D τ (T ) < ec(t ).Since T = T τ >T 1,thenD τ (T 1 )=D τ (T ). Thus, the minimum tax sufficient to induce adoption of the clean technology is obtained by setting D τ (T 1 )= ec(t ). A use of the dity technology enteing at time T = T τ eceives net benefits whose pesent value is, D τ (T 1 )= D(T e )=(a + bt 1 (p D1 + τ)) R T benefits of the last use of the clean technology is C(T e )= a p C 0 level sufficient to induce adoption of the clean technology is,. The. Theefoe, the tax e (t T ) dt = a+bt 1 p D1 τ τ m = bt 1 +(p C0 p D1 )=(b + zp D0 )T 1. (5) In ode to induce adoption of the clean technology at time T, the tax needs to be geate than the sum of the diffeence between the sevice pice of the two technologies, that is, p C0 p D1 = zp D0,andthebenefits of the installed base associated with the dity technology, that is, bt 1. If the netwok benefits of using the dity technology ae lage, then the tax equied to induce adoption will exceed the standad Pigouvian taxation, τ = ε. Fomally, τ m >τif (b + zp D0 )T 1 >ε. Pigouvian taxation could induce adoption only if the envionmental damages ae such that > D(T 1) C(T e ). Assuming that the dity technology has accumulated substantial netwok benefits at time T, all but a vey high tax will be ineffective and will only aise govenment evenue. Although the assumptions of the model ae vey estictive, not allowing existing consumes to espond to pice changes, they do eflect the obsevation that modeate levels of taxation have minimal effects on emissions. 20 20 Uses ae assumed homogeneous, all using thei automobiles with the same, inelastic intensity and theefoe, geneate the same amount of emissions egadless of pice. 11
4.2 Revenue neutal tax-subsidy policy 21 Fom equation (4) we know that adoption of the clean technology could be socially desiable even at modeate levels of envionmental damages. Thus, assuming (b + zp D0 )T 1 >ε, we conside a evenue neutal (balanced budget) policy in which the govenment eamaks envionmental tax evenues to subsidize the the clean technology afte time T. That is, the govenment levies a tax τ s on the dity technology fom peiod T τ, and commits to saving the evenues to subsidize the clean technology. We assume that the govenment etuns the tax poceeds as a subsidy s to each use of the clean technology, evey peiod fom T until some time T s afte which subsidization of the clean technology is not equied. Poposition 3 pesents the chaacteistics of this policy. Poposition 3 (i) When the govenment commits to use the evenues fom the tax on the dity technology to subsidize the clean technology within a evenue neutal policy, the equied tax to induce adoption of the clean technology is lowe elative to the case in which tax evenues wee used elsewhee in the economy. That is, τ s <τ m. (ii) The ates of the tax-subsidy policy ae τ s = B(b + zp D0 )T 1 and s = Aτ s,whee B<1 and A>0. Poof. (i) The pesent value of the net benefits that each use enteing at time T T and adopting the clean technology eceives is, C e s (T ) = C(T e )+ s R T s T e (t T ) dt = a p C 0 +s[1 e (Ts T ) ]. Substituting this into the condition fo adoption, that is, ec s (T ) D τ, yields the following elation between the tax and the subsidy, τ s (b + zp D0 )T 1 (1 e (Ts T ) )s. Assuming the condition holds with equality and utilizing equation (5) we can wite, τ m τ s =(1 e (T s T ) )s. (6) Theefoe, if s 0, thenτ m τ s. Assuming a balanced budget policy, the govenment s intetempoal budget constaint evaluated at time T τ is, Z Tτ Z Z T Z e (t Tτ ) T τ T τ s e (t T ) dtdt + τ s e (t T ) dtdt 0 T Z Ts h = e (T T τ ) s i T (1 e (T s t) ) e (t T ) dt. (7) The fist tem on the left-hand side of equation (7) is the pesent value of the total tax evenue obtained fom the existing uses of the dity technology. Since at T τ thee ae 21 We would like to thank an anonymous efeee fo pointing out the impotance of subsidizing the clean technology. 12
by assumption T τ uses of the dity technology and each of them pays a total of τ s,the value of the fist tem is τ s T τ. The second tem is the tax evenue collected fom new uses of the dity technology R fom T τ to T discounted to the time of govenment s decision T τ,thatis, τ s T T τ e (t Tτ ) dt = τ s (1 e (T T τ ) ). Each use enteing at any 2 T T and adopting the clean technology eceives a subsidy s pe peiod of time and the pesent value of he total benefits at time T is s R T s T e (t T ) dt = s(1 e (T s T ) ). Summing up the benefits of all the clean technology uses enteing fom time T until T s, discounted to time T, and then discounting this sum to the time of govenment s decision T τ, yields the ight-hand side of equation (7). The subsidy expenditue is e (T T τ ) 1 (1 + (T s T )) e (T s T ) s < s,sincebothe (T T τ ) and the 2 2 tem in backets ae less than unity. Substituting the above components into (7) and solving fo s yields s = Aτ s, (8) whee A = [(1+T τ )e (T Tτ ) 1] [1 (1+(T s T ))e (T s T ) ].22 Thus, the govenment s balanced budget equiement imposes the estiction that the tax ate is popotional to the subsidy. Whethe the tax is geate o smalle that the subsidy in any given peiod depends onthepolicy stimingandtheateofinteest. Fo the tax-subsidy policy to be evenue neutal and induce adoption of the clean technology, equations (6) and (8) should hold. Solving the system of these two equations yields, τ s = B(b + zp D0 )T 1, (9) whee B = 1 [1+(1 e (T s T ) )A]. Since (1 e (T s T ) )A>0, wegetthatb<1 and theefoe, τ s >τ m. The tax level sufficient to induce adoption of the clean technology is smalle when the geneated evenues ae used to subsidize the clean technology. Poposition 3 states that if the govenment commits to use the envionmental tax evenues to subsidize the clean technology fom T to T s, adoption of the clean technology could become the Nash equilibium at a lowe tax ate than in the absence of commitment.figue3illustatesthecaseinwhichtheequiedtaxtoinduceadoption of the clean technology within a evenue neutal policy equals the, exogenously given, envionmental damage, that is, τ s = τ = ε. The imposition of τ s on the dity good shifts the D cuve downwads to D τ fom time T τ onwads. The subsidy on the clean technology moves the e C upwads to e C s fom time T until T s.noticethatec s is not linea, because the net pesent value of the subsidy that the use eceives depends on time. Aea A 1 pesents the tax evenue eceived fom all uses of the dity technology at time T τ, which by the assumption 22 If taxes ae imposed at T τ = T and the subsidy is paid foeve, equation (8) educes to s = T τ s. If taxes ae imposed at T τ =0, equation (8) educes to s =(e T 1)τ s. 13
Benefits (a-p D0 )/+ (b+zp D0 )T 1 / (a-p C0 )/+ (1-e -(Ts-T*) )s/ = (a-p D0 -τ s )/+ (b+zp D0 )T 1 / τ s / ~ D = D A 1 A 2 ~ C s C B ~ C = C D τ ~ C (a-p C0 )/ T 3 T 1 T τ T * T s T 2 t Figue 3: Pigouvian tax and subsidy sufficient to induce adoption, within a evenue neutal policy of the model equals T τ. Aea A 2 is the (non discounted to peiod T τ ) pesent value ofthetaxevenuethatwillbeeceived fom all uses enteing fom T τ to T.Aea B is the (non discounted to peiod T τ ) pesent value of the subsidy expenses to all uses enteing fom T to T s. In ode to make the policy moe efficient, the govenment could choose to offe the subsidy fo a limited amount of time. The minimum subsidization peiod is detemined by the intesection of the D τ and the C e cuves, that is, Ts min =ag{d τ (T 1 )= ec(t s )}. The subsidy could be emoved at time Ts min since, afte that time, the clean technology s netwok has gown enough to guaanty that even without the subsidy the benefits to the uses enteing afte Ts min exceed the benefits fom adopting the old technology. D τ = ec(t s ) yields Ts min = T + T 1 (1 B). Since we have assumed that T 1 = T 2 T and we also know that 0 <B<1, itiscleathatthegovenmentcan eliminate the subsidy befoe the matuity of the clean technology s netwok. If the govenment decides to povide the subsidy fo the minimum amount of time, then by substituting Ts min into the values of B and A, the policy vaiables τ s and s ae deived as functions of the time of the tax intoduction, T τ. 14
h τ s i h i h B A Since τ s = B(b + zp D0 )T 1,thesign T τ = sign T τ = sign T τ i.fomthe definition of A we deive, A T τ = 2 T τ e (T s T ) < 0 whichthenyields τ s T τ > 0. Thus, the minimum equied tax is lowe the ealie is levied. Theefoe, the govenment could adjust the time of policy intevention, T τ such that the combination of tax and subsidy equied to induce adoption of the new technology involves a tax ate that equals the maginal extenal damage. 5 Conclusion This pape examined the choice of technology in the automobile maket in the pesence of netwok effects and envionmental extenalities. New uses aive at the maket evey peiod, each puchasing one automobile. The benefits that consumes deive depend on the numbe of consumes making the same choice, since the numbe of sevice stations incease with the numbe of uses of a paticula technology. We consideed two technologies: one that has developed a netwok of sevice stations and a second that is intoduced afte the matuity of the fist technology s netwok. The use of the established technology imposes envionmental damages on society while the new technology does not impose any envionmental cost. When the clean technology is intoduced, the dity technology is offeed at a lowe pice and has eached the maximum possible sevice netwok. We assumed that the clean technology netwok builds solely upon new uses. In the absence of any egulatoy intevention, we find that the clean technology will not be adopted. This is duetothefactthatthefist uses of the clean technology bea an excessively high shae of the costs and thus, they choose to puchase the dity technology. The pivate decision is welfae supeio when envionmental extenalities ae not pesent. Accounting fo the envionmental cost of the dity technology, the non-adoption equilibium may become socially inefficient. In such a case thee is need fo coective policy intevention. We fist examined the case of a tax on the dity technology. We found that the tax necessay to induce adoption of the clean technology is high and, in most cases, a Pigouvian tax will not be sufficient. Howeve, adoption of the clean technology is welfae impoving even at low levels of maginal envionmental damage. To addess these situations we examined the case in which the govenment commits to using the envionmental tax evenues to subsidize the clean technology within a balanced budget. We find that in this case the tax ate equied to induce adoption is lowe elative to the case of no subsidization. The esults of this pape could apply to othe cases whee envionmental extenalities and excess inetia can be obseved. Fo example, Cowan and Gunby (1996) povide two case studies to illustate how the agicultual maket can lock-in to the use of chemical contols fo pests elative to the claimed supeio method of integated pest management (IPM). To the extent that such a claim is valid, taxing chemical 15
contols and eamaking such taxes towads subsidizing supeio methods such as IPM could tilt the maket towads its adoption. Thee ae a numbe of diections in which the pesent analysis can be extended. In ode to allow fo patial esponse to envionmental taxation, the case of many heteogeneous agents enteing each peiod could be intoduced in the model. In such a case some of the consumes in each peiod could choose to not puchase the dity technology. Within this new famewok, optimal taxation could be examined that can esult in the adoption of the cleane technology. Anothe possible extension is to allow uses the choice of scaping the old technology and switching to the clean technology. Assuming that the value of the automobile depeciates, altenative policies could be examined, such as subsidizing the cost of switching technology. Futhemoe, the case of patially incompatible netwoks could be examined. As noted in the Intoduction, although thee is evidence of high degee of incompatibility, the possibility exists that existing gas stations could be tansfomed to hydogen filling stations. If the tansfomation of stations is complete, fo technical, secuity o legal issues, then the incease in the clean technology s netwok would imply a simultaneous decease in the dity technology s netwok. This would definitely acceleate the ate at which consumes switch technology. 6 Refeences 1. Athu W.B. (1989) Competing Technologies, Inceasing etuns, and lock-in by Histoical Events. The Economic Jounal, 99, 116-131. 2. Athu W.B. (1988) Self einfocing mechanisms in economics in The Economy as an Evolving Complex System, edited by P.W. Andeson, K.J. Aow and D. Pines, Repseus Books, Reading Massachusetts. 3. Califonia Ai Resouces Boad (2003) The 2003 Amendments to the Califonia ZEV Regulation. Available on line at http://www.ab.ca.gov/egact/ zev2003/fo.pdf. 4. Cowan, R. and P. Gunby (1996) Spead to Death: Pest Contol Stategies and Technological Lock in," Economic Jounal, 106, 521 542. 5. Cowan, R. and S. Hulten (1996) Escaping Lock-In: The Case of the Electic Ca." Technology Foecasting and Social Change, 53(1), 61-80 6. D Angelo A. and Z. Bilalis (2004) "Heading towads the hydogen economy", DG fo Entepise and Industy, Entepise Euope Newslette, No 16, July- Septembe 2004. 16
7. Depatment of Enegy (1999), Bluepint fo Hydogen Fuel Infastuctue Development. Washington DC. 8. Euopean Envionmental Agency (2000) Euopean Community and membe states geenhouse gas emission tends 1990-1998 Topic epot No 6/2000, July 2000. 9. EPA (1998) 1996 National Ai Quality and Emissions Tends Repot, Office of Ai Quality Planning and Standads, Januay 1998. 10. Faell J. and G. Salone (1985) Standadization, compatibility and innovation Rand Jounal of Economics, 16, 70-83. 11. Faell J. and G. Salone (1986) Installed base and compatibility Ameican Economic Review, 76, 940-55. 12. Foay, D. (1997) The Dynamic Implications of Inceasing Retuns: Technological Change and Path Dependent Inefficiency. Intenational Jounal of Industial Oganization, 15, 733 752. 13. Foeman-Peck, J. (1996) Technological Lock-In and the Powe Souce fo the Moto Ca. Discussion Papes in Economic and Social Histoy, 7, (Univesity of Oxfod) 14. Goodwin P, J. Dagay and M. Hanly (2004) Elasticities of Road Taffic and Fuel Consumption with Respect to Pice and Income: A Review. Tanspot Reviews, 24(3), 275-292 15. Katz M. and C. Shapio (1986a) Technology adoption in the Pesence of Netwok Extenalities. Jounal of Political Economy. 94(4), 822-41. 16. Katz M. and C. Shapio (1986b) Poduct compatibility Choice in a Maket with Technological Pogess. Oxfod Economic Papes, 38, 146-165. 17. Katz M. and C. Shapio (1985) Netwok Extenalities, Competition, and Compatibility. Ameican Economic Review, 75, 424-40. 18. Kisch, D. (2000) The Electic Ca and the Buden of Histoy, Rutges Univesity Pess, New Jesey. 19. Liebowitz S. J. and S. E. Magolis (1990) The Fable of the Keys. Jounal of Law and Economics, 33, 1-26. 20. Liebowitz S. J. and S. E. Magolis (1995a) Path Dependence, Lock-In and Histoy. Jounal of Law, Economics and Oganization, 11, 205 226. 17
21. Liebowitz S. J. and S. E. Magolis (1995b) Ae Netwok Extenalities a New Souce of Maket Failue? Reseach in Law and Economics, 17, 1 22. 22. Liebowitz S.J. and S.E. Magolis (1998a) Netwok Extenalities (Effects). enty in The New Palgaves Dictionay of Economics and the Law, MacMillan. 23. Liebowitz S.J. and S.E. Magolis (1998b) Path Dependence. enty in The New Palgaves Dictionay of Economics and the Law, MacMillan. 24. OECD (1997) Instuments: Taxation (i.e., cabon/enegy), Annex I Expet Goup on the United Nations Famewok Convention on Climate Change, Woking Pape No. 4. 25. Tietenbeg T. (1996) Envionmental and Natual Resouce Economics. Fouth edition, Hepe Collins College Publishes, New Yok, NY. 26. Unuh, G. (2002) Escaping Cabon Lock-In. Enegy Policy, 30, 317 325 7 Appendix (Poof of Poposition 1) Poof. Non-adoption is an equilibium if D(T ) e C(T ), and a unique equilibium if ed(t ) > C(T ). Since we focus on the case in which T >T 1,then,D(T )= ed(t )= ed(t 1 ). Theefoe, non-adoption is a unique equilibium if, ed(t 1 ) C(T )= b + p D 0 z T 1 1 1 e (T 2 T ) > 0. (10) Non-adoption is a unique equilibium if T 1 > 1 1 e (T 2 T ).SinceT 2 T = T 1 this inequality is witten as T 1 + e T 1 > 1, which holds fo all positive values of. 23 In tems of Figue 1, this poves that C(T ) cannot lie above the hoizontal line ed(t 1 ). The welfae diffeence between adoption and non-adoption is given by the net pesent value of the diffeence D(t) C(t), t, t [T, ), that is, fo all uses enteing afte the intoduction of the clean technology. Note that since we ae inteested in the case in which T >T 1,thent>T 1 and thus, D(t) = ed(t) = ed(t 1 ). Given the symmety in benefits and cost, it is appaent that afte the matuity of the clean 23 To simplify the exposition, denote by θ = T 1. Thus, we want to pove that θ + e θ > 1. It sufices to show that the minimum value that the expession θ + e θ admits is geate than 1. The fist deivative of the expession with espect to θ is, 1 e θ, which becomes zeo fo θ =0. Theefoe, fo θ =0the expession eaches its minimum value which is 1.Sinceboth and T 1 ae stictly positive, then θ>0, and the value of the expession is stictly geate than 1. 18
technology s netwok, the welfae diffeence is zeo. Thus, we ae concened with uses enteing the maket at time t [T,T 2 ).Thewelfaediffeence is, = b + p D 0 z = b + p D 0 z 2 W = Z T2 T µ T 1 1 Z T2 T D(t) C(t) e (t T ) dt (T 1 + T t) 1 1 e (T 2 t) e (t T ) dt (11) 1 e T 1 + µ e T 1 T 1 1 1 e T 1. The tem in the backets is positive and thus, non-adoption is efficient. 24 Theefoe, non-adoption is a unique and efficient equilibium if thee ae no extenal costs imposed by the dity technology. 24 To pove that the tem in backets is positive, we follow the same line of thought as in the pevious footnote. Denote by θ = T 1. The expession in backets eaches its minimum value of 0 fo θ =0. Since neithe no T 1 can be zeo, then θ>0, and the value of the expession is stictly positive. 19