Sustainable growth with renewable and fossil fuels energy sources

Transcription

1 Susainable growh wih renewable and fossil fuels energy sources Carlo Andrea Bollino and Silvia Micheli Deparmen of Economics, Finance and Saisics, Universiy of Perugia Via Pascoli 20, Perugia, aly Absrac ow o conrol climae change and o spur clean energy are among he mos imporan challenges facing he world oday. So far, a large srand of lieraure on climae change saes ha we need several economic policy insrumens o correc for exising ypes of marke failures, for insance, an environmenal ax on he carbon emissions and a research subsidy for research and developmen (R&D) in he renewable energy secor. We hink ha he failure of he exising policies on climae change is he fac ha implemenaion of renewable energy is spurred by flow of moneary subsidies o renewables price. Such a shor-run policy leads invesmen in renewables o be subopimal since invesors do no perceive climae change policies as a long lasing governmen commimen. We believe ha a more fruiful approach o ackle climae change should ake ino accoun ha invesors in renewable energy reac posiively o a sock of commimen and repuaion of he policy makers on he long run. To his end, he novely of his paper is consiued by modeling a sock of public capial which capures inensiy of governmen long erm commimen o suppor new echnology developmens. We consider a Schumpeerian model of endogenous growh o ake ino accoun ha producion emi polluans. The final good is produced employing labour and energy services from renewable energy and fossil fuels ha are imperfec subsiues. The quaniy of energy from fossil fuels is a funcion of invesmen and he amoun of resources exraced. n our framework, he price of he non-renewable energy follows he generalized version of he oelling rule. Concerning he renewable energy policy inervenion, we consider he effecive value of an innovaion paid o he invenor as an incenive for doing research in renewable energy in order o lower producion coss and make i compeiive in he energy marke. For doing so, we consruc wo varians since we ake ino accoun wo differen channels for governmen inervenion. n he firs varian, he producion funcion depends on invesmen and exising specific knowledge, ogeher wih a sock of public capial which represens he cumulaed governmen suppor o new echnology. n he second varian, he quaniy of renewable energy depends on he sock of knowledge and invesmen, which in urn depends on policy inervenion. There is he perspecive of a non-linear jump, ha is, here is a criical R&D hreshold beyond which renewable energy gains in imporance wih respec o he fossil fuels inpu. We firs presen he decenralized economy and sudy he behaviour of agens in each secor: he final good secor, he energy services, he consumers and he governmen. We characerize boh he decenralized equilibrium and he firs-bes opimum soluions. Nex, we show how he opimum can be implemened by an appropriae flow of public capial, comparing

2 he relaive effeciveness of curren moneary subsidies and governmen repuaion and commimens, in order o enable policy sraegies. Keywords: economic growh, energy, innovaion JEL codes: O44, Q48. nroducion There is an ongoing debae on he effeciveness of environmenal policies ino acion o ackle climae change. The concenraion of greenhouse gases (GG) in he amosphere was a 438 pars per million (ppm) of CO 2 equivalen in 2008, ha is almos wice he pre-ndusrial Revoluion level (EA, 2009). Such an increase is mainly caused by fossil fuel combusion for energy purposes in he power, indusry, building and ranspor secors (Sern, 2006). n a business-as-usual scenario, fossil fuel use is projeced o grow, and he diries fuel, i.e. coal, is expanding is share o face he rising in energy demand driven by developing. The global response o climae change sared wih he so called Rio Earh Summi in 992: governmens realized he need o work ogeher for an environmenal and susainable economic developmen. The Summi was a firs move owards boh environmenal and energy policies a global level, by seing he emission reducion arges for developed counries and esablishing a framework of wider reducion for he fuure from a susainable developmen poin of view. s weak poin was ha he Summi promised a lo and cos lile, since i was an agreemen wihou sringen measures (elm, 2008). The Summi has been followed by several discussions wih he purpose of finding opimal common environmenal policy for facing climae change. Aferwards, he Kyoo Proocol, an inernaional agreemen adoped in Kyoo on December 997, has commied (insead of encouraging) 37 indusrialized counries and he European Union (EU) o reduce GG emissions hrough naional measures. A large srand of lieraure on climae change saes ha we need wo economic insrumens o correc for he wo ypes of marke failures: an environmenal ax on he carbon emissions and a research subsidy for research and developmen (R&D) spillovers in he renewable energy secor (Bosei e al., 2009; Grimaud and Rougé, 2008). The carbon ax is needed because governmens mus increase he cos of polluion in order o reduce polluion generaion, so ha if i becomes more cosly, firms will produce less polluion. Since here are disorions in he economy and limiaions for governmen acions, we need oher insrumens in addiion o carbon ax o achieve he environmenal goals saed by inernaional environmenal agreemens, like subsidies o renewable energy. The renewable energy secor needs invesmen o encourage innovaion in echnologies and o achieve heir poenial. is expeced ha such invesmen will lead o a reducion of producion coss so ha renewable energies will be compeiive wih fossil fuels in he long run. n he renewable energy secor, every firm benefis boh from is own invesmen and from he knowledge spillovers ha come from he indusry. The benefis from R&D aciviies made by he represenaive firm may no be appropriable in ha here is no way 2

3 o exclude oher firms wihin he indusry from he new echnologies. Consequenly, here is no incenive for he represenaive firm o bear he expenses of invesmen. Moreover, here is he uncerainy wihin he energy indusry abou he level of invesmen in renewables made by he firms hemselves, so ha i migh be ha no one invess in he producion of energy from renewable resources. The reasons for public inervenion are hen sraighforward. The main policy insrumens used by counries are generally classified as price-oriened or quaniy-oriened. Some of hem are claimed o be more marke conform han ohers, while oher schemes are claimed o be more efficien in promoing he developmen of renewable energy (Meyer, 2003). Currenly, here is no general agreemen on he effeciveness of each scheme and we are sill far from enjoying he environmenal benefis coming from he use of renewable energy (eld e al., 2006). The bulk of lieraure on environmenal regulaion policies (Acemoglu e al., 2009; Grimaud and Rouge, 2008; Nordhaus, 2008; Quiggin and orowiz, 2003) focuses on he need of a carbon ax and a research subsidy o implemen he opimal environmenal policy. The model we propose ge underway from he one proposed by Grimaud e al. (200) in which hey basically show ha wo insrumens - an R&D subsidy and a carbon ax - are necessary o correc for he wo marke failures, i.e. R&D spillovers and polluion. We break wih radiion in relaion o he shor-run policies based on moneary subsidies he price of renewables. The failure of he exising policies on climae change is due o he fac ha he implemenaion of renewable energy is spurred by he flow of moneary subsidies o he price of renewables. Such a shor-run policy leads invesmen in renewables o be subopimal since invesors do no rus climae change policies: here are several urnabous on climae change policies ha suppor financially renewable energy in a shaky way, as i has happened recenly in USA, Germany, aly and Spain. We believe ha a more fruiful approach o ackle climae change should ake ino accoun ha invesors in renewable energy reac posiively o a sock of commimen and repuaion of he policy makers on he long run. As an example of credible long-run invesmen, consider ha he European nvesmen Bank has recenly creaed he 2020 European Fund for Energy, Climae Change and nfrasrucure ("Marguerie Fund") in parnership wih naional insiuional invesors wih he aim of financing energy infrasrucure on he long-run, wih emphasis o renewables (European nvesmen Bank, 200). The innovaion of he Marguerie Fund consiss of is aim ha i is no speculaive and i has a long-run horizon. The objecive of our paper is o show he effeciveness boh of a carbon ax and a flow of public capial which capures inensiy of governmen long erm commimen o suppor new echnology developmens insead of a subsidy o he price of renewables. To our knowledge, here is no a significan lieraure on his issue. We model an economy ha is made up of four producion secors: he final oupu, he energy services, he fossil-fuel secor and he renewable one. The combusion of fossil fuels generaes carbon dioxide (CO 2 ) ha damage he naural environmens and hen sociey. Furhermore, he producer of fossil fuels have a negaive cos from polluing emissions, unless he governmen inervenes wih marke insrumens like axes. n our model, he carbon and capure sorage (CCS) echnology ha allows for significan CO 2 emission reducions is included in he fossil- 3

4 fuel secor. The producive capaciy of fossil fuels is finie. According o he condiion derived by oelling (93), we describe he dynamic of he fossil fuels price ha is expeced o grow over ime. We assume ha here is research only in he renewable energy secor, because fossil fuels are exhausible and polluing. There are wo marke failures: polluion and research spillovers. The former is correced hrough a ax on he quaniy of polluion from fossil fuels. Research spillovers are relaed o he benefis from new green echnologies shared beween firms: innovaion is a non-rival good and i implies he inabiliy o exclude and o receive he social price of innovaion. We consruc wo varians since we ake ino accoun wo differen producion funcions. n he firs varian, he quaniy of renewable energy depends on invesmen and he sock of knowledge. The second varian evaluaes an alernaive producion funcion where a sock of public capial ener he producion funcion as an inpu, wih invesmen and he exising specific knowledge. We work on he effecive value of an innovaion paid o he invenor as an incenive for doing research in renewable energy in order o lower producion coss and make i compeiive in he energy marke. The effecive value of he paen for innovaion in he wo varians proposed changes according o he producion funcion of renewable energy. 2. The model The main feaures of model consis of a final oupu, which uses differen forms of energy as inpus, invesmen in energy efficiency augmening echnologies, R&D producing secor, socks of knowledge and sock of public capial, which capures inensiy of governmen long erm commimen o suppor new echnology developmens. The final oupu is produced using no-skilled labor, L, and energy services E : ( L, E ), where is increasing and concave in each argumen. We denoe by pe and w respecively he price of energy services and he real wage. The price of he final oupu is normalized o one. The profi of he represenaive producer is, w L pe, E. The firs-order condiions are: w 0 () L E p (2) E, 0 where F x is he derivaive of F wih respec o x. The energy services secor The amoun of energy and renewables E is produced from wo imperfec subsiues, ha are fossil fuels : E E(, ) where E is increasing and concave in each argumen. 4

5 Energy efficiency echnologies allow o reduce he conen of CO 2 from fossil fuels for an E amoun which is equivalen, in energy unis, o Z Z( ), where 0 Z. Denoing by p, and p, he prices respecively of fossil fuels and renewables, he profi funcion of he represenaive energy services producer is: E E, pe, E p, p, ( Z ), where is he ax paid by he energy producer in proporion o he polluing emissions ( Z ). The firs order condiions lead o: p E p ( Z ) 0 (3) E p E p 0 (4) E Z E 0 (5) The las one condiion allow us o evaluae he carbon ax ha is equal o, ha is he polluion ax depends upon he effor made by he represenaive firm o reduce emissions. The fossil fuel secor The fossil fuel secor depends on invesmen resources S exraced from ime. The dynamic of S is as follows: E Z in he fossil fuel secor, and on he amoun of S ds S (6) s 0 The fossil fuel producion funcion is (, S ), where is increasing in and decreasing in S. The profi of he fossil fuel producer is p. The maximizaion of he profi funcion subjec o he consrain (6) leads o he lagrangian L p and so he firs-order condiions are as follows: p 0 (7) p (8) S S where is he muliplier associaed wih (6). The erm S goes o zero due o he ransversaliy condiion. From equaion (7) we ge p ; differeniaing i wih 5

6 respec o ime, we ge p 2 and hrough eq. (8) we obain 2 S p p ha is he classic oelling rule. The renewable energy secor We analyze wo differen renewable energy producion funcions varians in order o sudy he effeciveness of wo differen governmen insrumens o implemen renewables among energy porfolio. n boh varians here exiss an R&D secor where he knowledge producion funcion is he same. We analyze he R&D secor, by focusing on he value of a paen for invenors of new green echnologies as a chance o swich o renewables insead of fossil fuels. Because of he naure of innovaion ha is a non-rival good, he price received by he invenor is differen from he social value of innovaion. The insananeous social value of an innovaion is,,, a a a ha is he sum of he marginal profiabiliy in he renewables secor plus he marginal profiabiliy of his innovaion in he renewables R&D secor. By inegraing he insananeous social value of an innovaion hrough ime, we ge he opimal value of a s rx dx paen A, a, s e ds (9) Now, consider he effecive value of he innovaion as a, a, where is a share of he social value which is effecively paid o he innovaor and 0. s rx dx The ineremporal effecive value is A, A a, e ds (0) s Differeniaing equaion (0) wih respec o ime, we ge: s ru du s ( ) 0 A a a e r ds A a r A which means r A A () a A Equaion () equals he rae of reurn of he innovaion on he financial marke o he rae of reurn of R&D aciviies. 6

7 Revering back o he R&D secor, he knowledge producion, of he invesmen knowledge. The profi funcion in he R&D secor is R&D secor supplies innovaions We can rewrie he profi funcion as is a funcion - he effor - in R&D secor, plus he sock of specific a price A which means ha he A and demands some invesmen ha is. A ( L, ) (2) The firs order condiion leads o: A 0 A (3) The marginal profiabiliy of innovaion is wrien combining he derivaive of he profi funcion wih respec o he knowledge sock, and equaion (3): a A (4) So, in order o obain he insananeous effecive value of he innovaion in he renewables R&D secor, we need he marginal profiabiliy in he renewable energy secor. n he firs varian, we consider ha renewable energy producion funcion is made up of hree inpus: invesmen in renewables, sock of exising knowledge and public capial G. The producion funcion wries (, G, ) wih increasing and concave in each argumen. G is he cumulaed governmen effor o suppor in he long run renewable energy and includes boh he acual value of policy commimen in moneary resource and he shadow value of he regulaory legislaion, which creaes a favorable adminisraive framework for invesmen decisions. We ge he marginal profiabiliy in he renewable energy secor hrough he combinaion of he firs order condiion of he R&D profi funcion wih respec o he invesmen public capial G. The profi funcion in he renewable energy secor is and he p (, G, ) (5) and he firs-order condiion wih respec o he invesmen and yields: 7

8 G 0 p 0 p 0 pg G and (6) (7) Then, he effecive value of he innovaion in renewables R&D secor in he firs varian of he model is: a, G (8) n he second varian, we discard he assumpion abou he exisence of sock of public capial considered in he renewable energy producion funcions, so ha his laer is no more using hree inpus as before, bu only wo: invesmen in R&D aciviies knowledge so ha (, ). and he sock of We wan o compue he effecive value of he innovaion, ha is he price paid o he invenor for doing research in renewable energy secor in order o subsiue fossil fuels wih renewables in he inpu porfolio energy services. We have already compue a, in he firs case; he mechanisms is more or less he same, bu we have o ake ino accoun ha he producion funcion of renewable energy producers now is differen. There is no more he public capial as an inpu, bu he governmen inervenion is modeled as a subsidy o invesmen, which is se 0. The profi funcion in he renewable secor is now: p (, ) ( ) (9) The firs-order condiion is: 0 p ( ) 0 0 p (20) (2) and combining equaions (20) and (2) we ge he marginal profiabiliy in he renewable energy secor: a, ( ) (22) We can wrie he effecive value of an innovaion in renewables R&D secor when governmens subsidize invesmen in renewable energy secor hrough a subsidy as: 8

9 a 2, (23) We can now compare equaion (8) ha is he effecive value of innovaion paid o invenors in he firs varian ( a ( a 2,, ) and (23), i.e. he effecive value of innovaion in he second varian ) o evaluae he bes insrumen in erms of subsidy o be associaed wih he carbon ax so ha renewables can overake fossil fuels in he long erm. We firs find he condiion for a a : 2,, G ( ) 0 F (23) and by reducing we ge G ( ) G 0 if ( ) (24) Then, we sudy he derivaive of he effecive value of innovaion wih respec o he policy insrumen (G in he firs varian and σ in he second varian). By doing he derivaive of he effecive value of an innovaion in equaions (8) and (23) we ge respecively a G GG (25) a (26) Eq (24) shows a quie plausible resul, i.e. we ge a beer effec of he capial sock G wih respec of he direc subsidy σ, when he produciviy effec of he public sock G ( G ) is relaively sronger han he produciviy effec of knowledge sock ( ), he higher is he subsidy share. n fac, if σ = 0 han a beer effec of he capial sock is graned if he lhs raio is > ; conversely, if σ =, hen i suffices a very small posiive G o saisfy condiion (24). This laer resul is raher obvious, because if he subsidy is covering he full amoun of invesmen, han here is no effecive value o innovaion. We can appreciae his poin noing ha boh expression (25) and (26) are negaive, i.e. an increase in public subsidy reduces he effecive value of innovaion, because firms will raher adop exising echnology if here is a subsidy. 9

10 Thus, comparing (25) and (26) we can see ha he negaive invenion value effec of he subsidy is less harmful in equaion (25) han equaion (26), if: GG (27) We can inerpre his laer resul saing ha he public sock G is relaively less likely han curren subsidy σ o incur in he risk of choking innovaion wih over subsidizaion, because GG is likely o be generally weaker han, being a second order effec (in fac, if is linear in G, han GG =0 and so (27) shows ha G is an absolue bes policy insrumen o spur invesmen in innovaion, ha is in research. 3. Theoreical resuls By aking ino accoun he firs varian proposed in he model ha is more aracive han he second one, we wan o show he dynamic sysem. Consider he social planner s problem: choose 0 L and E so as o: max U( C, V ) e d s.. (2) C ( L, E) (22) S (, ) V Z bvt 0 L L where V represen he dynamic of clean environmen which eners he uiliy funcion, and b is he sponaneous regeneraion rae according o which clean environmen evolves. The curren-value amilonian for he maximizaion problem is: U( C, V ) e C ( L, E) 2 3 (, ) 4 ( Z bv ) where, 2, 3 and 4 are he shadow prices of l, S, and V. Necessary firs order condiions for an inerior opimal soluion are: 0

11 : Ue C C : U C e L L : U C e E E E E 2 4 S 2 : 3 3 : U e V V Defining 3 b h, ha is he shadow price of environmenal qualiy in erms of knowledge in renewable secor, and d he depleion rae, we can derive he dynamic sysem: S 4 3 U e b U e b h h V 4 V 3 3 V Z bv ds S ds The equaions above consiue a dynamic sysem in S, V and h. 4. Conclusion Our analysis is relevan in he curren debae on he opimal climae change policy o implemen he use of renewable energy insead of fossil fuels. The main policy insrumens used by counries are generally classified as price-oriened or quaniy-oriened. Some of hem are claimed o be more marke conform han ohers, while oher schemes are claimed o be more efficien in promoing he developmen of renewable energy. Currenly, here is no general agreemen on he effeciveness of each scheme and we are sill far from enjoying he environmenal benefis coming from he use of renewable energy. We have shown ha a more fruiful approach o ackle climae change should ake ino accoun ha invesors in renewable

12 energy reac posiively o a sock of commimen and repuaion of he policy makers on he long run. For his purpose, we model a sock of public capial which capures inensiy of governmen long erm commimen o suppor new echnology developmens. We focus on he effecive value of innovaion paid o invenors of new green echnologies as an incenive for doing research in renewable energy ha make i compeiive in he energy marke. Such value varies according o he renewables producion funcion, and given he same burden in acual moneary erms for he Governmen, he main resul of he paper is ha policy is more effecive when he flow of public capial eners he producion funcion as a public sock compared o he moneary subsidies o energy prices. References Acemoglu D., Aghion P., Burszyn L., emous D., The environmen and direced echnical change. NB Working Paper no. 545 Aghion P., owi P., 998. Endogenous growh heory. The MTT Press, Cambridge MA. Bosei V., Carraro C., Massei E., Sgobbi A., Tavoni M., Opimal Energy invesmen and R&D sraegies o sabilize amospheric greenhouse gas concenraions. Resource and Energy Economics, vol.3, n.2, pp Elbasha E., Roe T., 996. On endogenous growh: he implicaions of environmenal exernaliies. Journal of Environmenal Economics and Managemen, vol. 3, pp European nvesmen Bank (EB), 200. European Fund for Energy, Climae Change and nfrasrucure, EB Press Release, Luxembourg Grimaud A., Laffourgue G., Magné B., 200. Climae change miigaion opions and direced echnical change: A decenralized equilibrium analysis. Resource and Energy Economics, Aricle in Press. Grimaud A., Rougé L., Environmen, direced echnical change and economic policy. Environmenal and Resource Economics, vol.4, no.4, pp Groh C., Ricci F., 20. Opimal growh when environmenal qualiy is a research asse. Research in Economics, aricle in press. eld A., Ragwiz m., aas R., On he success of policy sraegies for he promoion of elecriciy from renewable energy sources in he EU. Energy & Environmen, vol.7, no.6, pp elm D., Climae-change policy: why has so lile been achieved? Oxford Review of Economic Policy, vol.24, no.2, pp oelling., 93. The economics of exhausible resources. Journal of Poliical Economy, vol.39, pp

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