Elements of air pollution policy analysis

Transcription

1 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, Thess Appendx Elements of ar polluton polcy analyss The Natonal Research Councl has ponted out that more ways need to be explored to lnk scentfc research effectvely wth polcy and envronmental decson-makng a. One approach would be to promote nterdscplnary efforts desgned to gve scence graduate students an opportunty to work n a collaboratve effort, such as wth economsts and poltcal scentsts, to fulfll a project stuatng new envronmental research wthn a broader socal context. Ths appendx summarzes the results of work done n collaboraton wth Profs. Ingela Alger and Frank Gollop n the Economcs Department at Boston College. In t we consder elements of ar polluton polcy analyss, leadng to a novel perspectve on the effect of permt tradng (a popular market mechansm of polluton control) on pollutng frms competng mperfectly. A.1 Introducton Once scence has provded a seres of facts revealng the rsks assocated wth atmospherc consttuent concentraton levels, t becomes the task of governng agences to desgn approprate polces to safeguard ctzens aganst newly revealed threats. The role of government s crtcal n ths aspect as t alone can ntervene n the event of a market falure (see below). Ths dscusson of ar polluton polcy wll proceed from a bass of well-accepted market prncples, as seen n basc texts on mcroeconomcs 1,2. a NRC, Opportuntes n Appled Research and Development, Washngton, D.C.,1997, p.x. 147

2 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, Supply and demand If there were no polluton assocated wth the consumpton of energy, the prce of energy n a compettve (deregulated) market would reflect the equlbrum pont of market supply and demand. We explan that concept here brefly. On the supply sde, energy producers generate power at an output that wll maxmze ther profts. On the demand sde, energy purchasers consume at a rate that maxmzes the utlty of energy consumpton, subject to budget constrants. In a fully compettve market, demand and supply keep pace wth one another, settlng at a certan market prce. If producers were to over-produce (produce more than the market demands at that prce), prces would decrease due to overabundance, forcng frms profts down and thus motvatng a decrease n output. If producers were to under-produce, prces would ncrease due to scarcty, motvatng an ncrease n output. In ether case, convergence on equlbrum output s obtaned. It follows that compettve energy prces reflect consumers wllngness to pay for a partcular consumpton rate. In ths way, the prce mechansm reflects the aggregate preferences of ndvduals for a gven consumpton rate of energy. A.1.1 Market externaltes A polcy desgned to safeguard human health therefore does so n addton to what consumers have already decded s healthy or preferred through the prce mechansm. In 1970, the US Congress enacted the Clean Ar Act. Ths was n response to a body of evdence suggestng that buldup of SO 2 from power plant emssons was leadng to acd ran that was n turn harmng farmlands and buldngs. The publc knowledge of ths fact dd not decrease consumpton of energy from power plants. The Clean Ar Act was necessary because the ncreased costs mposed on constructon, agrculture, and health 148

3 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, programs due to energy consumpton dd not show up explctly n the prce of energy. Such hdden costs of consumpton are known as externaltes, negatve effects that cannot be mtgated by the prce mechansm alone. For such externaltes, the free market s unable to maxmze socal welfare, even when each consumer s aware of what hs or her consumpton s dong to socety as a whole. Epdemologcal studes n recent years have shown as many as 50,000 deaths per year n the U.S. can be attrbuted to urban ar polluton, 3 largely a result of emssons from power plants. Ths apparent loss n socal welfare s clearly beyond the reach the prce mechansm, and thus consttutes a sgnfcant externalty of energy consumpton. Such externaltes persst n a free market due to the so-called free rder problem, whch s assocated wth publc goods such as clean ar 4. Each ndvdual s bankng on every other ndvdual actng n the nterests of the whole, such that they see themselves as makng only a neglgble negatve effect n actng n ther own best nterests, wthout regard to the whole. When sgnfcantly deleterous externaltes are present, the government has some optons on how to offset the effect. We lst them here: 1) A command and control strategy s the tradtonal method of choce. The regulatng authorty smply ssues a control, sgns t nto law, and enforces t. 2) In addton, taxes can be leved on goods whose consumpton ncreases the level of the externalty. 3) Government subsdes can be ssued to help those enterprses whose success would offset the effect of an externalty, such as enterprses n renewable energy. 4) A more recent mechansm for controllng externaltes nvolves tradng permts n whch rghts to produce the product 149

4 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, whose consumpton causes the externalty are bought and sold on an open market. We dscuss ths mechansm n detal. Polluton permt tradng An mportant market-based approach to offsettng externaltes was ntroduced n 1968 by J. H. Dales. He proposed a system of polluton permts where the regulatory authorty decdes on a maxmum emsson level for whch a representatve number of permts s ssued. Each permt represents a rght to emt a certan quantty of pollutant over a gven perod of tme. These permts can be bought and sold on an open permt market. On the supply sde, the total number of permts s decded by the regulatng authorty and does not change wth prce. The EPA, for example may decde that 1 ton of SO 2 per month s the maxmum level of polluton allowable n the US. Pollutng frms would thus be requred to purchase polluton permts for the amount of pollutant they emt n a gven month, wth the total output of all frms automatcally capped at 1 ton. Ths would lead to effectvely hgher producton costs for drter frms compared to ther cleaner compettors, drvng down ther profts. Such frms would respond by decreasng output or nvestng n clean emsson technology, or both. A.1.2 Market neffcences due to mperfect competton In a perfectly compettve market, a permt tradng system as descrbed above can functon to offset the effect of externaltes such as those assocated wth energy consumpton. Ths concept has been developed and demonstrated theoretcally n the lterature 6,7. However, markets are rarely perfectly compettve, and a permt tradng system may lead to some non-ntutve effects on markets where the number of energy 150

5 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, producers s small enough that an olgopoly b s n place. To explore some potental consequences of a permt system when perfect competton does not preval, we wll look at the case of a duopoly, consderng the strategc nteractons between frms as they choose outputs so as to maxmze profts n permt tradng condtons. To our knowledge such strategc mplcatons of permt tradng have not been treated n the lterature. Because the number of energy frms servng a regon s typcally small, olgopolstc effects can be expected to play a role, such that predctons based on compettve models may be nadequate. We wll explore such olgopolstc effects by consderng the lmtng case of two frms. For ths, we ntroduce the noton of a Cournot duopoly. The Cournot duopoly model The 19 th century French engneer, Cournot, made an mportant advance n the theory of mperfect competton. We brefly descrbe the Cournot theory here, before applyng t to predct the outcome of olgopolstc effects under permt tradng. Consder two frms producng energy for a small regon. Frm 1 s an older frm usng mostly coal. Frm 2 uses a combnaton of coal and wnd from nearby wnd farms. Frm 1 s margnal costs of producton are less than that of Frm 2, but we wll assume ther total cost functons, c(y) have smlar functonal dependence on output, y. In ths dscusson c s the total cost for th frm for producton of output y, where y s a power producton (.e. klowatts) of the frm. Both frms face the market demand for energy. They may choose output levels, but not prces. We justfy that assumpton here. Subject to ther budget constrants, consumers wll only consume energy at a certan rate as a functon of ts prce. An b An olgopoly exsts whenever the number of frms n a market s too small to obtan the compettve supply and demand equlbrum descrbed above. 151

6 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, ncrease n prce leads to a decrease n consumpton. The demand curve s the map of prces (dollars/kw) as a functon of total power (kw) demanded. Snce frms sell everythng to maxmze revenue, producton equals consumpton at all tmes. Wth consumers preferences n place, the market demand for energy defnes how much wll be pad per kw for every output level of the producers. If power producton s very low, consumers are wllng to pay qute a bt per kw. As output ncreases, consumers pay less and less per kw. Ths demand curve s gven by p(y 1,y 2 ), where y 1 and y 2 are the power outputs of Frm 1 and 2 respectvely. If at any tme frms were to decde to ncrease prces at a certan output, they would dscover that consumers would smply buy less. In ths way, prces and quantty demanded are functonally lnked. Under ths assumpton, the role of the frms s then to choose outputs that wll maxmze ther profts. In the absence of government regulaton, taxes, subsdes, or permt tradng, the proft of the th frm s gven by: π = p y, y ) y c ( y ) (A.1) ( 1 2 Each frm knows that n order to maxmze profts, they must satsfy the followng at each perod: dπ dy = p c p( y1, y2 ) + y = 0 y y (A.2) We wll always assume that the proft functon has negatve concavty, such that the second dervatve s always negatve, and the above can be taken to occur at a global maxmum. Wth the demand curve gven by p(y 1,y 2 ), eq. A.2 can be solved for y (y j ), the output that Frm must choose to maxmze profts when Frm j chooses y j. Ths s known as Frm s reacton functon, as t predcts the response of Frm to an output choce of Frm j. As an example, consder the lnear demand functon: p(y 1,y 2 ) = 1-152

7 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, (y 1 +y 2 ). Consder also the ndvdual supply (cost) functons from the frms outputs to be gven by c (y ) = m y 2. Substtutng these expressons nto eq. A.1, we can show the reacton functon for the th frm to be: y 1 y j = (A.3) 2(1 + m ) Here, = 1 or 2 and j = 2 or 1, respectvely. Ths state of affars enables us to defne rules of a game wheren the players, Frms 1 and 2, compete wth one another to maxmze profts. In game theory, one makes the assumpton that players are fully ratonal, makng choces so as to maxmze payoffs. In the case where both frms choose output smultaneously, there exsts a par of outputs for the ratonal managers of the frms where the maxmum payoff s acheved. Ths occurs when each frm chooses an output that s optmal n the mdst of the other frm s optmal choce, a so-called Nash equlbrum 5. The concept of a Nash equlbrum was developed over a hundred years after Cournot, but Nash s dscovery revealed the Cournot equlbrum as belongng to a more general type. A Nash equlbrum n a two-player game s obtaned whenever each player s strategy s smultaneously a best response to the other s best response, maxmzng expected payoffs for both players 6. There exsts a par of outputs where nether frm wll have an ncentve to change. Such an optmum output, y* s defned when both y * 1 =y 1 (y * 2 ) and y * 2 =y 2 (y * 1 ), where y * 1 and y * 2 are the Cournot-Nash equlbrum outputs for Frms 1 and 2 respectvely. Ths s llustrated graphcally n fg. A-1 (as seen n Varan [1992]). 153

8 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, Frm 2's reacton functon 0.4 Frm 1's reacton functon Frm 1 Output Frm 2 Output Fgure A-1: Any choce of output not at the ntersecton of both frms reacton functons provdes ncentve for one of the frms to change the output choce. For example, f Frm 2 (downward slopng reacton functon) were to choose 0.45 as an output, Frm 1 would respond wth output choce 0.23, whch would provoke Frm 2 to choose 0.33, etc. Both Frms would quckly settle on the Cournot-Nash equlbrum, gven by the ntersecton, where nether would have an ncentve to change output. Applyng the deas outlned above, one can show that the equlbrum outputs wll be gven by: * 2m j + 1 y = (A.4) 4( m + 1)( m + 1) 1 j 154

9 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, Snce Frm 1 s drter, we may assume t costs less for t to produce the same amount of energy as Frm 2, such that m 1 < m 2. It follows that y 1 * > y 2 * as expected, snce ths frm pays less to produce a gven output of energy. It can be shown that the duopolsts ncrease ther combned producer surplus at the cost of the consumer surplus, resultng n a loss n socal welfare when compared to the compettve equlbrum wth large numbers of frms. 7 A.2 Permt tradng between duopolsts The effcency of a system of permt tradng n compettve markets s well establshed 8,9. In such a market, a permt tradng system can functon to offset the effect of externaltes such as those assocated wth energy consumpton. However, markets are rarely perfectly compettve, and a permt tradng system may lead to some non-ntutve effects on markets where the number of energy producers s small enough that an olgopoly s n place. To explore some of the features of a permt system when perfect competton does not preval, we wll look at the case of a duopoly, consderng the strategc nteractons between frms as they choose outputs so as to maxmze profts. We wll begn wth the assumpton that each frm beleves that the regulatng authorty wll check ther emssons at each perod. If they are found to emt more durng a perod than ther permts allow, they are very heavly fned. For now, we wll assume that no frm s wllng to chance beng caught n volaton of regulaton mandate. The new proft functon of each frm s gven by: π = p ) ε ( y1, y2 ) y c ( y x (A.5) 155

10 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, Here, ε s the market prce for emsson permts, and x s the number of permts bought or sold by Frm. Snce the frms are at all tmes constraned by the regulaton, they are requred to always own enough permts n a gven perod as to allow whatever emssons are assocated wth ther energy output durng that perod. In other words, each frm must satsfy: x ω y (A.6) Here, ω s a polluton coeffcent lnkng a frm s energy output to the amount of harmful emssons (.e. tons SO 2 / klowatt hour). In ths case, snce Frm 2 s newer and gettng a fracton of ts energy from wnd for example, we assume ω 2 < ω 1. The proft maxmzng permt-tradng duopolst must decde two mportant quanttes at each perod: the energy output and the number of permts to buy or sell. For now we wll assume that each frm s able to buy or sell permts nstantaneously, such that they may do so solely to accommodate the chosen output. In such a scenaro, f t turns out to be proftable to produce more output n a gven perod, the frm s not requred to have permts n reserve to accommodate the output ncrease. They buy when they need them and sell when they do not, wth no tme lag, and thus no rsk of beng fned by the regulatng authorty. Snce we also assume the prce of permts to be fxed, ths removes any ncentve for frms to save up permts, ether as fnancal nvestments or as a means of ncreasng flexblty of energy output. We wll look for a Cournot-Nash equlbrum usng the same method as descrbed n sec. A.1.2. We frst derve a reacton functon for each frm, revealng the optmal 156

11 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, choce n output (and permts to own) n response to that frm s belefs regardng the other frm s output choce. For a proft functon havng a parabolc shape such as eq. A.5 (quadratc n y ), the addtonal term due to permt tradng consttutes a vertcal translaton of the proft functon. As long as frms satsfy eq. A.6, they wll choose outputs as descrbed by the classc Cournot duopoly equlbrum, unhndered by the new regulatory constrant. Ther profts wll be larger snce they can sell unused permts, but ther choce of output wll be the same. If on the other hand, a frm fnds that the proft maxmzng choce s n volaton of regulaton (eq. A.6), t must make a new proft maxmzng choce. Ths s shown graphcally n fg. A-2. Purchasng new permts allows them to shft the constrant, represented by the vertcal lne, to the rght. Such a purchase however, shfts the proft functon down, such that the new proft functon (dependng on the number of permts bought) creates a new parabola (dashed lne). 157

12 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, Proft Output Fgure A-2. Permt tradng creates a new proft functon (dashed lne) for frms competng n a duopoly. Both profts and output decrease wth the permt tradng mechansm n place. Mathematcally, the optmum number of permts to buy s gven by maxmzng eq. A.5, subject to the constrant, x = ω y. Substtutng the constrant for y, a new proft maxmum s sought as a functon of x : dπ dx 1 x = (, ) + p c p x y j ε = 0 ω ω x x (A.7) Ths leads to a reacton functon for Frm as a functon of the expected output of Frm j. Usng the cost and market supply functons from before as an example, we obtan: x ω (1 ωε y j ) = 2(1 + m ) (A.8) 158

13 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, In ths case, t s apparent that ω plays an mportant role n determnng how many permts a frm wll choose to buy. Also, a low margnal cost coeffcent, m, (reflectng the fact that drty energy s usually cheaper) wll lead to an ncrease n the permts Frm must purchase. But n the case where both frms are forced to buy permts, Frm j s choce of output s constraned at y j =x j /ω j, such that we may wrte the permt purchase reacton functon or (equvalently) the output reacton functon of each frm as: x y x j ω (1 ωε ) ω j = 2(1 + m ) 1 ωε y j = 2(1 + m ) (A.9) (A.10) We can solve ether of these for the Cournot-Nash equlbrum as before to show: y * 1+ εω j + 2( m j εω εωm = 3 + 4( m + m + m m ) j j j ) (A.11) At ths equlbrum output c, nether frm has an ncentve to change ether the number of permts purchased or the energy produced n a gven perod. Dscusson Everywhere n A.11 where one frm s output s affected by the propertes of the other frm, we see evdence of strategc nteracton servng to couple each frm to the other. In the compettve equlbrum model of perfect competton, the frm need only worry about ts own polluton coeffcent or producton costs n decdng ts output. The market c It should be noted that n the case where only one frm s constraned by permts, there wll be a dfferent equlbrum. 159

14 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, would decde the rest. In the case of the duopoly, one frm s choces are explctly a functon of ts compettor s polluton/cost propertes, as well as ts own. If one were to allow permt prces to vansh, eq. A.11 becomes equvalent to eq. A.4 as expected. Makng permts free s dentcal to not requrng ther use, so we recover the no-permt case seen n the frst example. From eq. A.11 t s apparent that n the lmt of costless permts, the polluton coeffcents, ω drop out and the drter frm wll agan produce more. As ε ncreases however, the mportance of the ω-terms ncrease. To compare outputs of the old and new frms (1 and 2 respectvely), we focus our attenton on the numerator snce the denomnator s the same for both. Ignorng the 1 n the numerator, there are 4 terms remanng. For Frm 1, term 1 s low snce Frm 2 has a lower polluton coeffcent. Thus, Frm 2 s low polluton coeffcent wll have a tendency to drve down Frm 1 s output choce. The second term for Frm 1 however s larger than that for Frm 2 snce Frm 1 s producton costs are hgher. Ths term wll tend to drve up Frm 1 s output as expected. Term 3 for Frm 1 s hgh however, on account of ts very own hgh polluton coeffcent. Ths counters the 2 nd term, drvng down output. The fnal term s hgh on both accounts (Frm 1 s hgh polluton coeffcent and Frm 2 s hgh producton costs) and consequently drves Frm 1 s output even lower. In summary, ths expresson shows how producton costs drve hgh outputs for drter frms n the lmt of very cheap permts, and how polluton coeffcents can offset that effect, drvng down output (and profts) when permt prces become sgnfcant. 160

15 Taken from doctoral thess, Chemcal Knetcs and Mcrophyscs of Atmospherc Aerosols, copyrght by James W. Morrs, Appendx References 1 H. Varan, Mcroeconomc Analyss, (W.W. Norton & Company, New York, 1992). 2 W. Ncholson, Mcroeconomc Theory, (Dryden Press, 1998). 3 Report by the Amercan Wnd Energy Assocaton, G. Hardn, Scence, 162, (1968). 5 John Nash, Proceedngs of the Internatonal Academy of Scences, 36, 48-49, H. Gnts, Game Theory Evolvng, A Problem-Centered Introducton to Modelng Strategc Interacton, (Prnceton Unversty Press, Prnceton, 2000, 6). 7 Varan, p W. Baumol and W. Oates, The Theory of Envronmental Polcy, (Cambrdge Unversty Press, Cambrdge, 1988). 9 D. Pearce and R. Turner, Economcs of Natural Resources and the Envronment, (Johns Hopkns Unversty Press, Baltmore, 1990). 161