The effectiveness of taxation and feed-in tariffs

Transcription

1 The effetiveness of taxation an fee-in tariffs Fabio Antoniou an Rolan Strausz

2 The effetiveness of taxation an fee-in tariffs Fabio Antoniou an Rolan Strausz May 12, 2014 Abstrat We stuy (energy) markets with irty inumbents an ostly entry by lean prouers. For intermeiate entry osts, the market outome exhibits ineffiient proution an ineffiient entry. A poliy mix of three popular regulatory instruments taxation on polluters, fee-in tariffs for lean entrants, an taxation of onsumption annot orret these two market failures. Fee-in tariffs an onsumption taxes are ineffetive instruments for implementing the first best. The seon best requires fee-in tariffs or onsumption taxes. For a given level of proution, the instruments are ineffetive in influening the overall buget, but may be effetive for other bugetary onepts. Keywors: taxation, fee-in tariffs, externalities, entry, pollution JEL oes: D21, D61, H23 Humbolt-Universität zu Berlin, Institute for Eonomi Theory 1, Spanauer Str. 1, D Berlin (Germany), fabio.antoniou@wiwi.hu-berlin.e. Humbolt-Universität zu Berlin, Institute for Eonomi Theory 1, Spanauer Str. 1, D Berlin (Germany), strauszr@wiwi.hu-berlin.e. We thank Panos Hatzipanayotou, Carsten Helm, Ulrih Kameke, Kai Konra, Maro Runkel, Ronnie Shöb, an Anastasios Xepapaeas for helpful isussions an suggestions. Both authors gratefully aknowlege finanial support by the BMBF in projet "CReW". 1

3 1 Introution We point out that a urrently popular 1 ombination of regulatory instruments taxation on polluters, fee-in tariffs for lean entrants, an taxation of onsumption is unable to ahieve the joint poliy goal of internalizing externalities of irty inumbents an inuing effiient entry of lean prouers. These instruments are therefore imperfet. As a result, we ontrait the urrent poliy ebate, whih argues that it represents the right poliy mix for attaining these goals. At first sight our results may seem surprising, beause the lassi Tinbergen rule of one instrument per poliy objetive suggests that the mentione poliy mix shoul be able to reah the two poliy goals. Beause there are atually three instruments, one may even see room for a thir poliy goal: balaning the buget to finane the intervention sheme. Inee, the poliy ebate offers the following intuitive reasoning how to obtain these three goals: Use the tax on the polluting inumbents to aress the externality problem, use the fee-in tariff to alleviate the entry problem, an, finally, use the onsumption tax to balane the buget. The poliy mix, therefore, seems to supply the perfet tool box for ealing with the two market imperfetions. We aution that the above reasoning is misleaing an argue that the set of instruments is muh less effetive. We erive our results in a market setup with irty inumbents an ostly entry by lean prouers. In this setup, the entrant s inentives to enter are suboptimally low, simply beause he isregars the ontribution to soial welfare that is appropriate by the onsumer surplus. Consequently, our market setup represents a minimalist setup for moeling the problem isusse in the poliy ebate: the externality problem of the irty inumbents an too little inentives for entry by lean prouers. For this market setup, we first of all show that fee-in tariffs an onsumption taxes are ineffetive instruments for inuing the first best. More preisely, we show that a soial planner is just as well off between using only a tax on polluters or only using a ombination of fee-in tariff an onsumer taxation. Put ifferently, if the soial planner an attain the effiient outome with the three instruments, she an also reah it with only a tax on polluters (or alternatively, only with a ombination of fee-in tariff an onsumer taxation). Hene, om- 1 Fee-in tariffs are urrently applie by more than 50 ountries, inluing the US, Canaa, most of the European ountries, an China. 2

4 plementing a tax on polluters by a fee-in tariff, a onsumption tax, or a ombination of the two is reunant. The reason for this failure is a market interation of the instruments, whih prevents their use as inepenent poliy instruments. As a onsequene the usual Tinbergen logi fails. We further show that, for intermeiate entry osts, no set of instruments exist that inues effiient proution an effiient entry. This establishes the imperfetness of the set of instruments for aressing the two poliy goals. Sine these poliy instruments are in general unable to ahieve the first best, we further stuy the seon best. Intuitively, it traes off reutions in the inumbent s irty proution against inuing entry. In orer to inue entry, the seon best istorts upwars the proution of the potential entrant to enable it to reover its entry osts. Interestingly, the seon best overorrets the polluter s output by inuing a proution level below the effiient one. Overall proution in the seon best is nevertheless istorte upwar. A soial planner an ahieve this seon best with a tax on irty proution an a fee-in tariff that subsiizes entry. Hene, only with regar to the seon best, the fee-in tariff beomes an effetive, albeit suboptimal instrument. In aition to these two instruments, the onsumption tax is however still reunant in that it oes not enable the soial planner to attain a higher welfare than using only the polluter tax an the fee-in tariff. Sine the seon best alloation uniquely etermines the buget, we also obtain that the onsumption tax is also ineffetive in balaning the buget of the overall set of instruments. Our results aution against putting too muh hope in the set of instruments as urrently use in one way or another by many governments. For instane, the Saninavian ountries implement an expliit emissions tax, while the European Union implemente suh a taxation sheme iniretly through its three phase program of traable emissions permits. An alternative sheme with similar effets is a tax on energy proue by the polluters from whih renewable soures are exempte. The latter has been implemente in the Unite Kingom, Germany an the Netherlans. Quota obligations equivalent to market share requirements were establishe in Italy, Denmark, Belgium, Australia, Austria, Sween, the Unite Kingom an many U.S. states (Fisher an Newell, 2008). In the ontext of our setup, all these shemes are equivalent to the introution of an expliit polluter tax. Regaring the entry problem of the lean prouers, the European Commission (2008 p.3) views fee-in tariffs as most effetive ealing with entry osts: "Well-aapte fee-in 3

5 tariff regimes are generally the most effiient an effetive support shemes for promoting renewable eletriity". 2 Unersoring this view, European Commission ( 116b, 2013) proposes as a guieline for aiing immature tehnologies that "Ai is grante by way of a fee-inpremium". 3 Nowaays, fee-in tariffs are applie by more than 50 ountries suh as the U.S. where the iniviual states set their own tariffs, Canaa, most of the European ountries, with Germany being the leaer, an China. 4 Finally, the politial arena is also muh onerne about the funing of these intervention shemes an espeially the fee-in tariffs. Some ountries use a revenue-neutral system whih reovers tariff expenitures by either a surharge on the eletriity prie, or alternatively, by a general government tariff (Lehmann, 2013). The first has been applie by most of the ountries an puts the buren solely to the eletriity onsumers. The seon one, whih has been implemente in the Netherlans, translates to a buren to all taxpayers. Relate literature: Although poliy makers stress the ommon poliy goal of effiient proution an effiient entry of lean prouers, environmental eonomis has not really fouse on these two issues simultaneously. Stuies on fee-in tariffs abstrat from the isrete zero-one eision of entry an o not moel a ost of entry of the lean energy prouers (e.g., Shneier an Gouler, 1997; Fisher an Newell, 2008; Aemoglu et al., 2012; Reihenbah an Requate, 2012; Lehmann, 2013). These papers fous, instea, on the marginal effets on investment inentives an analyze how fee-in tariffs mitigate externalities ue to learning by oing an spill-over effets in R&D. 5,6 Although we view these aitional externalities as important, we point out that they apture a ifferent problem than entry. 2 See e Jager an Rathmann (2008), International Energy Ageny (2008), an Deutshe Bank (2012) for similar views. 3 Some authors istinguish fee-in tariffs from fee-in premiums, viewing a tariff as a guarantee prie of proution, whereas the premium is a fixe markup over the market prie. Although there is an important ifferene in its pratial implementation, there is no real eonomi ifferene between the two an we use the woring "tariff" inisriminately. 4 A etaile view of these poliies aross the U.S. states an several European ountries an be foun on the following links:< 5 Although not mentione expliitly stuies by Jaffe et al. (2005) an Helm an Shöttner (2008) also support promoting poliies for similar reasons. 6 Using ata from OECD ountries, Nesta et al. (2014) fin empirial support for the hypothesis that urrent renewable energy poliies foster green innovation. In a Nori ase stuy base on win power, Boomsma et al. (2012) verify that the fee-in tariff enourages earlier investment. 4

6 In ontrast, stuies like Spulber (1985), Katsoulaos an Xepapaeas (1995) an Requate (1997) fous speifially on the problem of optimal entry uner negative proution externalities. They however o not aress the role of ifferent poliy instruments in stimulating the entry of lean versus irty prouers. Given our fous on the entry problem, we follow the latter approah (an muh of the literature in inustrial organization) an expliitly moel the entry ost of lean prouers. These entry osts may omprise the evelopment osts of new tehnologies, the osts of setting up the new proution failities, or some alternative fixe osts. 7 In ontrast to the existing literature on fee-in tariffs, we abstrat from any spill-over effets. This enables us to attribute our results an insights about the unerlying eonomi mehanisms unambiguously to the joint problem of effiient proution an effiient entry, on whih the poliy ebate fouses. It further allows us to ifferentiate our paper learly from the aforementione stuies on feein tariffs. We however point out that spill-over effets woul atually exaerbate our entry problem. Beause next to the onsumer surplus, the entrant will also not take into aount the positive spill-over effets of its entry, spill-overs istort the entrant s entry eision further away from effiieny. There is a vast literature in publi eonomis on the effetiveness of ifferent Pigou-tax bases when ealing with both single an multiple market failures. In the ontext of (environmental) externalities, Palmer an Walls (1997), Shöb (1997), Walls an Palmer (2001), an Fullerton an Wolverton (2000; 2005) point out that instea of taxing the polluter, a soial planner may equivalently tax other partiipants. Fullerton an Wolverton (2005) ombine this with revenue onsierations of the government. This result is muh in-line with our result that in orer to implement the first best, the regulator may either only tax the polluter or equivalently use a ombination of fee-in tariff an onsumer taxation. In line with the lassi Tinbergen rule, ealing with multiple market failures usually requires a mix of ifferent poliy instruments. In the ontext of environmental externalities, Fisher an Newell (2008), Gouler an Parry (2008) an Garia et al. (2012) for instane 7 For example in the speifi ontext of energy markets, pratitioners view these fixe entry osts as taking the lion share of overall proution osts of lean prouers. For instane, US Energy Information Aministration (Table 1, 2013) reports that the geothermal, win, or solar generation of eletriity involve no substantial variable osts an mainly fixe osts. Similarly, the European Win Energy Assoiation (2009) omputes that the setup osts for establishing a win powere plant typially aounts for the 75% of its total osts. 5

7 argue that multiple instruments are neee to aress all the relevant imensions. This stans in ontrast to our insight that, when the first best is feasible in the presene of two imperfetions, a single emission tax suffies to orret both market imperfetions at the same time. Sine this result no longer hols in the seon best, our results are more in line with the literature on the seon best use of multiple poliy instruments suh as Bennear an Stavins (2007). Finally, there is a growing literature on the ynami impliations that may arise from the introution of these poliies (e.g., Grafton et al an Hintermann an Lange 2013). Suh ynami onsierations are however orthogonal to the issues we aress an our moel therefore abstrats from those ones. As alreay argue by Petrakis et al. (1997), entry in a ynami environment effetively implies that the firm an the soial planner ompare the isounte profits to the entry osts. Hene, if the soial planner an the entrant have a ommon isount fator, then aing ynamis to our framework woul not lea to any aitional effets. If, in ontrast, the soial planner has a smaller isount fator than the firm, then the entrant s entry hoie is further istorte ownwars, whih, in our framework, effetively means that the entry problem is intensifie. 2 Setup Consier an inustry that proues a homogeneous goo x, for instane eletriity. The representative onsumer has a quasi-linear utility an obtains a utility Ψ(x) from onsuming a quantity x. His utility is inreasing in onsumption at a ereasing rate, i.e.,ψ (x)>0an Ψ (x)<0. We normalizeψ(0)=0. The inustry onsists of an inumbent, irty setor. The irty setor proues the goo with a ost funtion C (x ), whih is inreasing an onvex, i.e., C (x )>0 an C (x )>0. Moreover, as an inumbent there are no entry osts, i.e., C (0)=0. The inumbent setor uses a irty tehnology in that a proution x imposes a negative externality E(x ), whih is inreasing at a (weakly) inreasing rate, i.e., E (x )>0 an E (x ) 0. Moreover E(0)=0. In aition to the irty tehnology, a new, lean tehnology is available, but its use requires an entry ost of F 0. The lean setor proues with a ost funtion C (x ), whih is inreasing an onvex, i.e., C (x )>0 an C (x )>0. 8 Sine F represents the fixe ost of 8 Note that onvex ost funtions also esribe orretly proution tehnologies with a onstant marginal 6

8 proution, we have C (0)=0. In orer to guarantee internal solutions, we aopt the Inaa onitions,ψ (0)=C ( )= C ( )=,Ψ ( )= C (0)=C (0)= E (0)=0. Fousing on the externality an entry problem, we abstrat from any ompetitive problems an assume that ompetition poliy is effetive so that firms at as uner full ompetition. 9 Before analyzing the market outome, we first haraterize the effiient outomes. 3 Effiient Outomes In this setion, we erive the effiient proution levels an an upper boun on the ost of entry below whih it is effiient. In orer to obtain these results, we ompute, an subsequently ompare, the levels of output that maximize soial welfare with an without entry. Given onsumption x, proution x of the irty setor, an proution x of the lean entrant, soial welfare gross of entry osts is W(x, x, x ) Ψ(x) C (x ) C (x ) E(x ). Sine feasibility requires x= x + x, effiient, first best proution levels(x f b, x f b ) solve max x,x W(x + x, x, x ) F 1 x >0 with 1 x >0 the iniator funtion, enoting whether the entry osts F are pai, whih epens on whether entry (x > 0) takes plae or not. Hene, if entry is soially esirable, then the first best levels(x, x ) satisfy Ψ (x + x )= C (x )+ E (x ) anψ (x + x )= C (x ). (1) If, in ontrast, entry is not soially esirable, then the first best levels(ˆx, ˆx ) satisfy Ψ (ˆx )=C (ˆx )+ E (ˆx ) an ˆx = 0. (2) Defining F W(x + x, x, x ) W(ˆx, ˆx, 0), a iret omparison of the welfare levels uner(x, x ) an(ˆx, 0) yiels the following result: ost up to some fixe apaity. 9 Clearly, this is an iealize starting point, but presents a lear benhmark an allows us to isolate the problems that are only ue to the externality an entry problem an not onfoune by other eonomi problems suh as imperfet ompetition. 7

9 Proposition 1 Entry is soially esirable an first best levels exhibit(x, x ) if F F. Otherwise entry is not esirable an first best levels exhibit(ˆx, 0), where x < ˆx < x + x = x. Hene, entry is only soially effiient if the ost of entry is small enough an F represents the exat threshol level below whih this is the ase. Moreover, the effiient level of the irty setor is smaller with entry than without entry, whereas overall effiient level of proution is larger with entry. These results are all in line with stanar intuition. 4 Ineffiient Market Outome In this setion we onsier the outome of an unregulate market an ientify the istortions from the first best. Let p represent the market prie for eletriity. Consumers maximize their net onsumer surplus Φ(x) Ψ(x) px. Hene, the onsumers eman funtion D(p) obtains from the first orer onition p=ψ (x). The irty setor maximizesπ (x )= px C (x ). Consequently, the supply funtion S (p) obtains from the first orer onition p=c (x ). Given entry, the lean entrant maximizesπ (x )= px C (x ). The supply funtion S (p) follows from the first orer onition p=c (x ). Our Inaa onitions together with our onvexity assumptions imply that the first orer onitions are suffiient an lea to well-efine an positive eman an supply for any p>0. Given that entry ours, the ompetitive equilibrium prie p satisfies D(p )=S (p )+ S (p ) an the equilibrium outome is x = D(p ), x = S (p ), x = S (p ) with p =Ψ (x )=C (x )= C (x ). (3) In this market equilibrium, the profit of the entrant isπ = p x C (x ) F an is positive if F F, where F p x C (x ). Proposition 2 A ompetitive market equilibrium with entry exists only if F F. In this equilibrium, the irty setor s output is larger than in the first best(x > x ); the entrant s output is smaller than in the first best(x < x ); an the overall output is larger than in the first best (x > x ). Moreover, it hols F < F. 8

10 The proposition ientifies the usual istortions in a market with a negative externality. Overall proution x is too large ompare to the first best, beause the market fails to internalize the negative externality. Consequently, the polluting firm proues too muh at the expense of the lean entrant, whih proues too little from an effiient point of view. The proposition, moreover, shows that the entrant s inentives to enter the market are istorte ownwar(f < F ). The reason of this ownwar istortion is that the entrant s profit is smaller than its ontribution to total welfare. In partiular, it annot extrat its ontribution to the onsumer surplus. Depening on the entry osts F, we may therefore lassify the ifferent market failures as follows: 1. For low entry osts, F F, the market leas to an externality problem, but not an entry problem. 2. For intermeiate entry osts, F (F, F ), the market leas to both an externality problem an an entry problem. 3. For high entry osts, F F, the market leas to an externality problem, but not an entry problem. 5 The Poliy Instruments In this setion we introue the poliy instruments by whih the regulator an aress the externality an entry problem. In partiular, the regulator may use three regulatory instruments: 1. a (speifi) tax t on the irty proution; 2. a fee-in tariff t to subsiize the entrant s lean proution; 3. a (speifi) tax, t ψ, on the onsumer s onsumption. We isuss first the effet of the poliy instruments(t, t, t ψ ) on the market outome. The instruments affet the market outome, beause they hange the effetive pries whih market partiipants fae. Given a market prie p, the tax t on the irty setor implies that irty firms effetively fae a prie p t for eah unit sol. As a result, the profit-maximizing supply is S (p t ), where C (S (p t ))= p t. Similarly, the fee-in tariff t effetively raises the lean prouer s return to p+ t for eah unit so that, onitional on entering the market, it optimally supplies S (p+t ), where C (S (p+t ))= p+t. Finally, the onsumption 9

11 tax t ψ raises the onsumers prie to p+ t ψ. Hene, market eman is D(p+ t ψ ) an satisfies Ψ (D(p+ t ψ ))= p+ t ψ. For a given set of regulatory instruments(t, t, t ψ ), the equilibrium prie with entry, p r, satisfies D(p r + t ψ )=S (p r t )+S (p r + t ). Consequently, we say that the instruments(t, t, t ψ ) implement an alloation(x, x ) with x > 0 if an only if there exist some prie p r suh that x + x = D(p r + t ψ ); x = S (p r t ); x = S (p r + t );Π r (x )=(p r + t )x C (x ) F 0. (4) As isusse in the introution, a soial planner may also have bugetary onerns. Given a set of instruments an an equilibrium prie p r, the overall buget of the poliy mix is B t ψ D(p r +t ψ )+ t S (p r t ) t S (p r +t ). (5) Conition (4) restrits the poliy outomes(x, x ) that are implementable, an thereby limits the effetiveness of the instruments. The following lemma gives a haraterization of these limitations. It will play a ruial role for our subsequent results. Lemma 1 Instruments(t, t, t ψ ) implement the alloation(x, x ) with x > 0 if an only if (i) t ψ =Ψ (x + x ) C (x ) t =Ψ (x + x ) C (x )+ t ; (ii) Entrant s profits areπ r = C (x )x C (x ) F 0; (iii) Consumers net surplus isφ r =Ψ(x + x ) Ψ (x + x )(x + x ); (iv) Inumbent s profits areπ r = C (x )x C (x ); (v) The buget equals B=[Ψ (x + x ) C (x )]x +[Ψ (x + x ) C (x )]x. The lemma follows iretly from onition (4) an expresses the remaining egree of freeom in the use of the instruments when implementing a ertain alloation. The result obtains beause given a set of instruments(t, t, t ψ ) the equilibrium prie p r aapts so that eman equals overall supply. Hene, the market interation of the instruments limits their use for implementing ertain alloations. 10

12 p p p S + E S + S + E S + S + + : F + : F r : F D ˆx x x x Figure 1: Effiient an Market Outomes 6 First Best: Failures an Reunant Instruments In this setion we show two of our main results. First, the three regulatory instruments are imperfet in that they are unable to ahieve the effiient solution in general. Seon, the fee-in tax an the onsumption tax are reunant in that they o not help to ahieve effiient outomes. To establish these results, we first efine F r C (x )x C (x ). We may then aapt Lemma 1 to obtain the following result. Proposition 3 It hols F < F r < F. Moreover, (i) For F (F r, F ) a set of instruments implementing the effiient outome fails to exist. (ii) For F (F r, F ) a set of instruments whih implements the effiient outome exists. For any suh set of instruments, it hols t ψ = t = E (x ) t an the net onsumer surplus, profits, an the bugets are uniquely etermine. Moreover, one suh set of instruments exhibits t = E (x ) an t =t ψ = 0. The proposition states first of all that the entrant s inentives to enter are higher in a regulate market that implements the effiient outome than in the unregulate market, but still too low from an effiieny point of view. As alreay explaine in our isussion of Proposition 2, the entrant s inentives to enter the market are too small as ompare to the first best, beause its profits are smaller than its ontribution to total welfare. Figure 1 illustrates this more learly. The market equilibrium in an unregulate market obtains where eman D equals the aggregate supply funtion S + S. This yiels the equilibrium prie p an total 11

13 output x. At this outome, the entrant s profit gross of entry osts, F, is the area between the urves S +E an S +S +E up to p, beause the ifferene between these urves equals the entrant s marginal osts. For the effiient outome however, the eman urve D equals the sum of aggregate supply funtion S + S plus the marginal externality E. As a result, the effiient output x is smaller than the unregulate market outome x an the effiient outome obtains for the larger prie p. The entrant s gross profit, F r, orrespons again to the area in between the urves S + E an S + S + E but now up to the higher prie p. As a result, F < F r. Yet, also at the prie p, the entrant oes not extrat its entire ontribution to overall welfare. As illustrate by the triangle in Figure 1, the onsumers extrat a part of the entrant s ontribution in the form of a larger onsumer surplus. Consequently, it follows F < F r < F. Statement (i) of the proposition substantiates our laim that the three regulatory instruments are imperfet. They are, in general, unable to ahieve the joint poliy goals of effiient proution levels an effiient entry. In partiular, the first best outome an only be ahieve, when the entry problem is non-existent F (F, F ) or small F (F, F r ). Statement (ii) of the proposition explains the sense in whih the fee-in tariff an the onsumption tax are reunant for implementing effiient outomes. First of all, if the effiient outome is not attainable with only a tax t on irty proution, it is also not attainable by using the fee-in tariff an the onsumption tax as aitional instruments. Moreover, these two instruments o not help in alleviating the buget or ajusting the profits or net onsumer surplus. These results follow beause when implementing the effiient outome, the instruments leave only a small egree of freeom in their use. In partiular, the fee-in tariff must oinie with the onsumption tax. Moreover, the fee-in tariff an the polluter tax must a up to the marginal externality at the first best output level. Hene, the freeom in the use of instruments to inue effiient outomes is highly restritive. In partiular, any set of poliy instruments for whih the fee-in tariff iffers from the onsumption tax, oes not inue an effiient outome. Consistent with usual results, effiieny obtains with the usual tax sheme where only the irty proution is taxe by the marginal externality, t = E (x ), while onsumers are not taxe at all an the lean entrant reeives no fee-in tariff, t ψ = t = 0. Yet, an alternative way to implement the effiient outome is not to tax irty proution at all, t = 0, but equate the 12

14 onsumer tax an the fee-in tariff to the marginal externality: t = t ψ = E (x ).10 Hene, if the effiient outome is attainable, then a regulator may also ispense with taxing the externality an attain it by using only a fee-in tariff with a mathing onsumption tax. In aition, when the polluter tax, for some reason, oes not math the marginal externality, a regulator may use an appropriate fee-in tariff an mathing onsumption tax to orret for this. 11 For intermeiate entry osts, F (F r, F ), the instruments fail to implement the effiient outome. We therefore onlue that the set of instruments is imperfet. There are two possible ways to pursue. First, we an ask whether there exists a ifferent set of instruments whih enables the implementation of effiient outomes. Seon, we an lower our goals an hange our fous from first best effiieny to seon best outomes by asking the question what is the onstraine optimal use of these imperfet instruments. 7 Seon Best: Charaterization In this setion, we stuy the onstraine effiient use of the three instruments, when they annot implement the effiient outome but no alternative set of instruments exist. We haraterize seon best outomes, whih maximize soial welfare over those outomes that are implementable by the three instruments. The seon best outome solves a trae-off between inuing entry an regulating the externality an we erive it by omparing the welfare maximizing implementable alloation without an with entry. We show that also with respet to the seon best the three poliy instruments exhibit a reunany. The seon best is attainable by using only two of the three instruments. Moreover, the reunant thir instrument is ineffetive in regulating the sheme s buget. It is straightforwar to see that the seon best without entry(ˆx sb sb, ˆx ), oinies with the effiient outome without entry as efine in (2):(ˆx sb sb, ˆx )=(ˆx, 0). Inee, this outome 10 In a ifferent setup, this egree of freeom is also note in Palmer an Walls (1997), Shöb (1997), Walls an Palmer (2001), an Fullerton an Wolverton (2000; 2005). 11 For instane, the raft of the Guielines on environmental an energy ai for , mentions in paragraph (108) that "the EU ETS an national CO2 taxes internalise[...] may not (yet) ensure the ahievement of the relate, but istint EU objetives for renewable energy[...] the Commission therefore presumes that a resiual market failure remains, whih ai for renewable energy an aress." 13

15 maximizes soial welfare among all outomes without entry. It is attainable, beause the regulator an always prevent entry by a negative fee-in tariff. We next aress the welfare maximizing implementable outome with entry,(x sb, x sb ). This outome is a solution to the onstraine maximization problem max x,x W(x + x, x, x ) s.t. C (x )x C (x ) F 0. Disregaring the onstraint yiels the outome x = x an x =x as efine in (1). It violates the onstraint if F> F r. Sine the problem is onave, the onstraint then bins at the optimum. From this observation we obtain the following insight. Proposition 4 For F (F r, F ), the seon best alloation(x sb, x sb ) with entry exhibits (i) C Ψ (x sb sb sb (x )x (ii)ψ (x sb (iii) x sb C (x sb )= F; + x sb )=C sb (x )+ E (x sb); > x, x sb < x an x sb = x sb + x sb > x + x = x ; (iv) it is implementable with the set of instruments(t sb, tsb + x sb )+ tsb ψ tsb = ψ E (x sb ) tsb., tsb ψ ), where tsb = C sb (x ) For F > F r, the output x is too small to yiel enough profits to ompensate for the entry osts F. The seon best with entry, therefore, exhibits an output of the lean entrant that is istorte upwar so that the fixe osts is overe, (x sb > x ). It then remains to etermine the output level of the irty setor that given the entrant s output x sb, eals with the externality effiiently. As the quantity of the entrant rises, the marginal benefit from onsumption ereases. As a result, the output of the irty setor is lower than in the first best (x sb < x ), beause at the effiient proution level, the marginal benefit from onsumption equals the soial marginal osts. Finally, overall proution in the seon best with entry is larger than the orresponing one in the first best. Proposition 4(iv) further haraterizes the set of poliy instruments that implements the seon best alloation. In partiular, it shows that a polluter tax t alone is unable to attain the seon best. Consequently, a positive fee-in tariff is neee. A speifi set of instruments whih ahieves the seon best, is the usual externality tax that equals the marginal externality (t sb = E (x sb )) together with a positive fee-in tariff(tsb= C sb (x ) Ψ (x sb + x sb )>0). A further onsumption tax is not neee(t sb ψ = 0) so that the seon best is attainable with only two of the three instruments. Moreover, it is interesting to note to what extent the require set of instruments iffers from the set of instruments that implements the first best as esribe 14

16 0 F F r F sb F effiieny entry no entry market outome entry no entry 1st best regulation possible impossible possible optimal use 0 1st best entry F F r 2n best entry F sb 2n best no entry F 1st best no entry Figure 2: Outomes in Proposition 3(ii). Uner the seon best the optimal mix between the onsumption tax an the polluter tax follows the same rule as in the first best, i.e., the sum of the two taxes must be equal to the marginal externality at the targete pollution level. Yet, the fee-in tax must exee rather than equal the onsumption tax. Defining F sb W(x sb + x sb, x sb, x sb ) W(ˆx, ˆx, 0)< F, we an ompare the welfare levels assoiate with(ˆx, 0) an erive the optimal regulation (x sb, x sb ) in the seon best. Proposition 5 For F (F r, F sb ] the optimal use of instruments is to inue entry an outome (x sb, x sb ). For F (F sb, F ) the optimal use oes not inue entry an outome(ˆx, 0). Figure 2 ollets our results. Comparing the first an seon row reveals how the market istorts entry ownwar. The reason for this ownwar istortion is that, in a market, the entrant an extrat only a part of the effiieny gains from entry while inurring its full ost. It is therefore less willing to enter. The thir line shows that the three instruments are unable to ahieve the first best for intermeiate entry osts, while the fourth line emonstrates for these intermeiate osts, whether uner an optimal use of the instruments entry ours. 15

17 8 General effetiveness of the poliy mix Until now we onsiere the effetiveness of the instrument mix to implement either first or seon best alloations. In this setion, we stuy the general effetiveness of the instruments to inue some market outome with entry. This stuy allows us to argue that the at first sight intuitive argument presente in the introution the tax on irty proution is to aress the externality problem, the fee-in tariff is to alleviate the entry problem, an the onsumption tax is to balane the buget is misleaing, beause the three instruments exhibit an inherent epeneny. To show this, the next proposition states to what extent the restritions of Lemma 1 limit the effetiveness of the poliy instruments with entry in general. Proposition 6 Suppose an outome(x, x ) with x > 0 is implementable by a set of instruments (t, t, t ψ ) an yiels net onsumer surplusφ, profit levelsπ,π, an a buget B. Then, (i)(x, x ) is also implementable by only a tax t an a fee-in tariff t an yiels the same net onsumer surplusφ, profit levelsπ,π, an buget B. (ii)(x, x ) is also implementable by only a tax t an a onsumption tax t ψ an yiels the same net onsumer surplusφ, profit levelsπ,π, an buget B. The proposition shows a general reunany in the poliy instruments. With respet to the market outome, net onsumer surplus, iniviual profits, an the overall buget, it suffies to use only two of the three instruments. Given that the regulator uses a tax t either the fee-in tariff t or the onsumer tax t ψ is superfluous. Hene, the regulator an o just as well by using only two instruments instea of three. The proposition, moreover, implies that we annot use the three poliy instruments inepenently for regulating the externality, ensuring entry, an buget onerns. The proposition therefore explains in what sense the Tinbergen logi of the introution fails an that the intuitive argument presente in the introution the tax on irty proution is to aress the externality problem, the fee-in tariff is to alleviate the entry problem, an the onsumption tax is to balane the buget is inorret. Finally, we want to note that the buget irrelevane of the instruments as ientifie in Proposition 6 epens on the exat onept of the buget. In some ountries that implement the polluter tax through a permit system, politiians seem more onerne with finaning only 16

18 the fee-in poliy through the onsumption tax. To aress this onern we efine a poliy mix(t, t, t ψ ) as fee-in buget balane if it implements an alloation(x, x ) so that t x = t ψ (x + x ). (6) For a poliy mix that is fee-in buget balane, the total expenitures assoiate with the fee-in tariff math the overall revenues from the onsumption tax. For poliy instruments that are fee-in buget balane, we obtain the following haraterization. Proposition 7 Suppose a sheule(t, t, t ψ ) implements an alloation(x, x ) with x > 0. Then there exists a poliy mix(t, t, t ) whih is fee-in buget balane an implements(x ψ, x ). In partiular, a poliy mix with onsumption tax t =(t ψ t ψ )x /x, polluter tax t = t +t ψ t. an fee-in tariff ψ t = t t ψ + t represents suh a poliy mix. ψ Although the proposition hols for any alloation(x, x ) with x > 0, its interpretation is markely ifferent epening on whether or not it is applie to the first best alloation (x, x ). With respet to the first best alloation, the proposition effetively implies that feein buget balane poliy instruments annot use fee-in tariffs or onsumer taxation. To see this, reall from Proposition 3(ii) that any set of instruments whih implements the first best requires t ψ = t. Given x > 0, suh poliy instruments only satisfy the fee-in buget balane onition (6) if t ψ = t = 0. Hene, any fee-in buget balane set of poliy instruments that implements the first best must use only a tax t (whih then equals the marginal externality) an oes not use a fee-in tariff or onsumer tax. In ontrast, the proposition ientifies a speifi role for onsumer taxation when implementing an alloation(x, x ) for whihψ (x + x ) C (x ). Suh alloations are neessarily ineffiient, but restriting to fee-in buget balane instruments, they o require a speifi non-zero onsumer tax. This onsumer tax is at most as large as the fee-in tariff. 9 Conluing Remarks The urrently popular ombination of regulatory instruments taxation on polluters, feein tariffs for lean entrants, an taxation of onsumption is, in general, unable to solve both externality an entry problems. Consequently this set of instruments is not the right one 17

19 for aressing these two problems. In ontrast, a tax on polluters that equals the marginal externality together with a lump-sum subsiy onitional on entry that overs the entry osts is an example of a set of instruments that inues the first best. From a poliy viewpoint suh fixe, quantity inepenent transfers may seem suspiious an iffiult to implement. 12 It woul however be naive to view the fee-in tariff as an aequate alternative to suh a lump sum transfer. The fee-in tariff is istortive, beause it affets marginal onsierations whereas the lump sum payment oes not. If regulation is restrite to the exlusive use of the three aforementione instruments, then regulation will, in general, only be seon best. This seon best poliy is suboptimal in that it either istorts entry ownwars or overshoots in reuing irty proution together with overproution in the lean tehnology. We stress that we obtain suh results alreay in our surprisingly parsimonious setup that aptures the essene of the externality an entry problem in a most elementary way. The plainness of our setup allows us to ientify learly the basi eonomi fore that the market interation of the poliy instruments restrits their effetiveness as inepenent poliy measures. We also point out that entry osts are an essential part of any framework where entry is a problem; the fat that potential entrants o not enter must mean that the benefits of entry the profits o not outweigh some kin of entry osts. For our arguments it oes not matter whether these profits or osts are unertain or ynami. It is also immaterial whether the entry osts reflet the evelopment ost of some new tehnology or some other more munane entry ost. Introuing aitional aspets, suh as for example imperfet ompetition, asymmetri information, spill-over externalities, or transbounary pollution, may lea to aitional effets whih, when strong enough, an affet our results. We onsier any suh extensions worthwhile, but point out that our insight of the basi limitations of the instruments ue to their market interation is a robust feature that will also play a role in more ompliate setups. 12 As alreay note in the introution, the European Commission ( 116b, 2013) avoates the use of fee-in tariffs to promote immature tehnologies an isourages the use of iret subsiies. 18

20 Appenix This appenix ollets the formal proofs. Proof of Proposition 1: Follows from a straightforwar omparison of the optimal welfare level with an without entry. In orer to show x < ˆx < x, efine the funtion x (a) impliitly by Ψ ( x (a)+a)=c ( x (a))+ E ( x (a)). (7) Note that x = x (x ) an ˆx = x (0). By the impliit funtion theorem it follows Ψ ( x (a)+a)( x / a+ 1)=C ( x (a)) x / a+e ( x (a)) x / a (8) so that x a = Ψ C + E Ψ < 0, where the inequality follows beause C an E are onvex anψ is onave. Hene, x is stritly ereasing so that x = x (x )< x (0)= ˆx. Note that sine C > 0, E > 0 an x / a<0 the right han sie in (8) is negative. SineΨ < 0 we must have x / a+1>0. Hene, the term x (a)+a is inreasing in a so that it follows ˆx = x (0)+0< x (x )+x = x. Q.E.D. Proof of Proposition 2: We first show x > x. We istinguish two ases: 1. If x > x, then it follows by applying (3), onvexity of C (x ), an (1) the hain of inequalities C (x )= C (x )> C (x )= C (x )+E (x )> C (x ). This inequality implies by the onvexity of C (x ) that x > x. 2. If, instea, x x, then x x woul imply x x, by whih we obtain the ontraition 0=2Ψ (x ) C (x ) C (x ) E (x )<2Ψ (x ) C (x ) C (x ) 2Ψ (x ) C (x ) C (x )=0, where the last equality follows from the FOCs whih efine(x, x, x ). We next show x < x. Suppose not, then x x an x > x imply x = x + x > x + x = x so thatψ (x )=C (x ) C (x )=Ψ (x ), whih ue to the onavity ofψ an only hol if x x, a ontraition. To show x > x note that, ue to x < x an the onvexity of C, it followsψ (x ) Ψ (x )= C (x ) C (x )<0. Hene,Ψ (x ) Ψ (x ). Conavity ofψ then implies x x. To show F < F efine p Ψ (x )=C (x )+ E (x ). Sine ˆx > x an x is suh that C (x )+ E (x )= p, we have C (x)+ E (x)> p for all x (x, ˆx ) ue to onvexity. 19

21 Moreover, sine ˆx < x an x is suh thatψ (x )= p, we haveψ (x)> p for all x (ˆx, x ), ue to the onavity ofψ. Consequently x ˆx [Ψ (x) p ] x+ Using this inequality it then follows ˆx x [C (x)+ E (x) p ] x> 0. x F = p x C (x )< p x C (x ) p x C (x )= [p C (x)] x (9) = p x x < p (x x ) x = = x 0 ˆx Ψ (x) x+ x 0 Ψ (x) x C (x) x= p (x x ) x 0 ˆx x x 0 C (x) x+ x [C (x)+ E (x)] x [C (x)+ E (x)] x 0 ˆx [Ψ (x) p ] x+ 0 C (x) x (10) x 0 x 0 ˆx x [C (x)+ E (x) p ] x (11) C (x) x (12) ˆx C (x) x Ψ (x) x+ 0 ˆx 0 [C (x)+ E (x)] x = W Ŵ = F, (14) where the two inequalities in the first line follow from p > p an reveale preferenes, respetively. (13) Q.E.D. Proof of Lemma 1: By efinition, the instruments(t, t, t ψ ) implement an alloation(x, x ) with x > 0 if an only if there exist some prie p r suh that (4) hols. The onitions in (4) are equivalent to the set of onitions Ψ (x + x )= p r + t ψ (15) C (x )= p r t (16) C (x )= p r + t, (17) Π r (x )=(p r + t )x C (x ) F 0. (18) " " Suppose(t, t, t ψ ) implements the alloation(x, x ). Then there exists a p r suh that (15)- (17) hols from whih it follows: Statement (i) follows from rewriting an ombining (15) an (16) as follows t ψ =Ψ (x + x ) p r =Ψ (x + x ) C (x ) t an rewriting an ombining (15) an (17) as follows t ψ =Ψ (x + x ) p r =Ψ (x + x ) C (x )+ t. 20

22 Statement (ii) follows beause entrant s profits areπ r =(pr +t )x C (x ) F= C (x )x C (x ) F 0, where the equality follows from (17). Non-negativity follows by (18). Statement (iii) follows beause onsumer s net surplus isφ r =Ψ(x + x ) (p r + t ψ )(x + x )=Ψ(x + x ) Ψ (x + x )(x + x ). Statement (iv) follows beause profits of the irty setor areπ r =(pr t )x C (x )= C (x )x C (x ), where the last equality follows from (16). Statement (v) follows from using statement (i), sine it thereby follows B=t ψ (x + x )+ t x t x =[t ψ + t ]x +[t ψ t ]x =[Ψ (x + x ) C (x )]x +[Ψ (x + x ) C (x )]x. " " Suppose (i) to (v) hols, then (18) hols by (ii). We therefore only have to show existene of a prie p r so that (15)-(17) hol. Take p r =Ψ (x + x ) t ψ so that (15) hols per onstrution. By (i) it then follows p r t =Ψ (x + x ) t ψ t =Ψ (x + x ) Ψ (x + x )+ C (x )=C (x ) so that also (16) hols. Moreover, by (i) it follows p r + t = Ψ (x + x ) t ψ + t =Ψ (x + x ) Ψ (x + x )+ C (x )=C (x ) so that also (17) hols. Q.E.D. Proof of Proposition 3: F < F r < F follows from the proof of Proposition 2, sine the right han sie of equation (9) equals F r. Statement (i) follows iretly from Lemma 1(ii). Statement (ii) follows iretly from Lemma 1(i) an (ii) ombine with the onitions for effiieny esribe in (1). Q.E.D. Proof of Proposition 4: (i) follows iretly, beause of the bining onstraint at the optimum. (ii) is the first orer onition of maximizing W(x + x sb, x, x sb ) with respet to x. To show (iii) note first that for F>F r the onstraint at x = x it follows x sb is violate. From this > x, beause the left han sie of the onstraint is inreasing in x, ue to C (x )x + C (x ) C (x )=C (x )>0. It follows moreover x sb= x (x sb)< x (x )= x with x (.) as efine in (7), where we showe that x (.) is ereasing but by less than 1. As a result x sb = x sb C + x sb > x + x = x. It remains to show (iv). From Proposition 4(ii) an Lemma 1 it follows t sb =Ψ (x sb ) sb (x ) tsb = ψ E (x sb instruments(t sb, tsb, tsb ψ ) tsb ψ an tsb =Ψ (x sb ) C sb ) implements(x, x sb (x sb ). Reall that x sb )+ tsb. Hene, by Lemma 1, the set of ψ > x an x sb > x an x is suh that C (x )=Ψ (x ). Convexity of C an onavity ofψ then imply C sb (x )>Ψ (x sb ) so that t sb > t sb ψ. Q.E.D. Proof of Proposition 5: Maximum welfare without entry equals W(ˆx, ˆx, 0), whereas max 21

23 imum welfare with entry equals W(x sb + x sb, x sb, x sb ) F. Hene, optimal regulation in- volves entry when F< F sb. Sine W(x sb W(x sb Q.E.D. + x sb, x sb, x sb )<W(x + x, x, x ) we have F sb = + x sb, x sb, x sb ) W(ˆx, ˆx sb, 0)=W(x + x sb, x sb, x sb ) W(x + x, x, x )+F < F. Proof of Proposition 6: Suppose(t, t, t ψ ) implements the outome(x, x ) with net onsumer surplusφ, profit levelsπ,π, an a buget B. By Lemma 1 any other set of instruments(t, t, t ) that implements(x ψ, x ) must also yiel the same net onsumer surplusφ, profit levelsπ,π, an a buget B. We therefore only have to show that the speifi set of instruments exist. To see instruments exist that satisfy (i). Set t = 0, ψ t =Ψ (x + x ) C (x ) an t = C (x ) Ψ (x + x ). It then follows by Lemma 1 that also(t, t, 0) implements(x, x ). To see instruments exist that satisfy (ii). Set t = 0, t ψ =Ψ (x + x ) C (x ), an t =Ψ (x + x ) C (x ) t = ψ C (x ) C (x ). It then follows by Lemma 1 that also (t, 0, t ) implements(x ψ, x ). Q.E.D. Proof of Proposition 7: Sine(t, t, t ψ ) implements(x, x ), it follows by the efinition of (t, t, t ) an Lemma 1 that ψ t = t + t ψ t ψ =Ψ (x + x ) C (x ) t ψ an t = t t ψ + t ψ = C (x ) Ψ (x + x )+ t ψ. It then follows from Lemma 1 that also(t, t, t ψ ) implements(x, x ). It remains to show that (t, t, t ψ ) is fee-in buget balane. This follows from t x =(t t ψ + t ψ )x =(t ψ x /x + t ψ )x =t ψ x + t ψ x =t ψ (x +x ). Q.E.D. 22

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