Envronmental Taxaton and Structural Change n an Open Economy A CGE Analyss wth Imperfect Competton and Free Entry Chrstoph Böhrnger, Henz Welsch and Andreas Löschel
Non-techncal summary The economc effects of envronmental taxes depend on the market structure. Under mperfect competton wth free entry and ext, envronmental taxes have an mpact on economes of scale by changng the number and sze of frms. Whether economes of scale rse or fall n a partcular ndustry depends on nduced changes n the prce elastcty of demand. Because export demand s more prce elastc than domestc demand, the overall prce elastcty rses (falls) as the ndustry gans (loses) n comparatve advantage. We use a computable general equlbrum model for Germany to examne the effects of a unlaterally ntroduced carbon tax under both perfect and mperfect competton. Our key fndng s that nduced structural change n favor of the less energy ntensve, more labor ntensve ndustres s more pronounced under mperfect competton than under perfect competton. At the macroeconomc level, the total costs of envronmental regulaton under mperfect competton can be hgher or lower than those under perfect competton dependng on whether aggregate gans or losses n economes of scale across mperfectly compettve sectors preval.
Envronmental Taxaton and Structural Change n an Open Economy A CGE Analyss wth Imperfect Competton and Free Entry by Chrstoph Böhrnger a, Henz Welsch b and Andreas Löschel c January 2001 JEL classfcaton: D43, D58, L13, Q25 Keywords: envronmental taxaton, mperfect competton, structural change We wsh to thank Vola Ehrenhem for preparng the data base. Fnancal support from the Volkswagenstftung under the project Umweltsteuern, nternatonaler Wettbewerb und Beschäftgung n enem Smulatonsmodell mt unvollkommener Konkurrenz s gratefully acknowledged. a Center for European Economc Research (ZEW), Mannhem, Germany b Department of Economcs, Unversty of Oldenburg, Germany c Center for European Economc Research (ZEW) and Department of Economcs, Mannhem Unversty, Mannhem, Germany
1. Introducton For decades, the theory of envronmental polcy has recommended envronmental taxes, or lkewse tradable emsson permts, on the grounds that they provde a cost-effectve means of envronmental regulaton. In vew of the need to combat global warmng and the relatve ease of desgnng an approprate tax scheme for CO 2 as the most mportant greenhouse gas, envronmental taxes have recently become popular n the poltcal arena, too. Several European countres have ntroduced envronmentally motvated taxes on energy, but most of these tax ntatves devate from the basc prncples of envronmental taxaton n varous regards. In addton to not beng based on the carbon content of dfferent energy carrers, tax schemes typcally nvolve reduced tax rates or tax exemptons for ndustres that are energy ntensve and/or export-orented. The motvaton for ths type of unequal treatment s the ntenton of protectng these ndustres aganst a loss n nternatonal compettveness (see e.g. Böhrnger and Rutherford 1997). From a theoretcal perspectve, t s evdent that a tax strctly n proporton to emssons mples a shft n comparatve advantage, dependng on the degree to whch several ndustres dffer n terms of emsson ntensty. What has been largely gnored, however, s that these shfts n comparatve advantage may be sgnfcantly renforced under mperfect competton where changes n market structure affect both producton costs as well as markup rates. Under condtons of mperfect competton wth free entry and ext, the number and sze of frms and, hence, ther ablty to explot economes of scale depend on the elastcty of market demand. If market demand s composed of domestc demand and export demand, each characterzed by a dfferent demand elastcty, the elastcty of total market demand wll depend on the shares of domestc sales and sales abroad. To the extent that envronmental taxes lead to a shft n comparatve advantage, these shares wll change, and so wll frm sze and unt costs,.e. economes of scale. Ths paper uses a mult-sector computable general equlbrum model for Germany to examne the mpacts of a unlateral natonal carbon tax under both perfect and mperfect competton on goods markets. Under mperfect competton, we fnd that economes of scale declne n ndustres whch lose comparatve advantage, whereas economes of scale ncrease n ndustres whose comparatve advantage mproves. The key to these results s the emprcal 1
evdence that the elastcty of demand s typcally hgher for sales abroad than for sales n domestc markets (Burnaux et al. 1992). 1 As a consequence of nduced changes n the economes of scale, the degree of structural change s larger under mperfect competton than under perfect competton. At the macroeconomc level, the costs of envronmental regulaton under mperfect competton turn out to be hgher than under perfect competton for the German economy, because on the whole the changes n economes of scale across mperfectly compettve sectors are negatve. Gven that any assessment of the structural effects of envronmental taxes n open economes s crucally affected by market structure and the nduced changes thereof, t s surprsng that the lterature seems to have largely gnored the mpact of envronmental taxes on market structure. Whereas general equlbrum models wth scale economes and endogenous market structure are standard tools n the analyss of trade polcy (see, e.g., Harrs 1984, Norman, Branson and Wnters 1990, Capros, Karadeloglou and Mentzas 1991, Wllenbockel 1994), envronmental economcs has mostly addressed market structure n a partal-equlbrum framework (see, e.g., the contrbutons n Carraro, Katsoulacos and Xepapadeas 1996), whch, by defnton, does not allow the analyss of structural change. An early envronmentally-orented computable general equlbrum model wth mperfect competton on good markets s presented by Conrad and Wang (1993), but n ths model, as n the partal equlbrum models, frm numbers and scale economes are fxed. The paper s organzed as follows. Secton 2 provdes a non-techncal overvew of our analytcal framework. Secton 3 presents the smulaton results and ther economc nterpretaton. Secton 4 summarzes and concludes. 2. The Model 2.1 General Framework Ths secton presents the man characterstcs of our comparatve statc mult-sector computable general equlbrum (CGE) model for the German economy, whch s desgned to assess the medum-run effects of carbon/envronmental taxes on trade and ndustral structure 1 Unlke the elastcty on the export market, the elastcty on the domestc market s derved from producton and consumpton elastctes whch are typcally less than one. See, e.g., Burnaux et al. (1992). 2
(see Appendx A for an algebrac model formulaton). The analyss covers 13 sectors and 3 prmary factors as descrbed n Table 1. The sectoral aggregaton captures key dmensons n the analyss of greenhouse gas abatement, such as dfferences n carbon ntenstes and the degree of substtutablty across energy goods and carbon-ntensve non-energy goods. The energy goods dentfed n the model are hard coal (HCO), lgnte (SCO), crude and refned ol (OIL), natural and manufactured gases (GAS) and electrcty and steam (ELE). The nonenergy sectors nclude mportant carbon-ntensve and energy-ntensve ndustres that are potentally most affected by carbon abatement polces, such as basc materals and chemcal products (MMC), nvestment goods (EQP) and transport (TRN). The rest of the economy s dvded nto agrcultural producton (AGR), consumpton goods (CSG), constructon (CST), prvate servces (SER) and publc servces (PUB ). Prmary factors nclude labor (LAB), captal (CAP) and fossl-fuel resources (RES). Labor and captal are treated as perfectly moble across sectors whereas fossl-fuel resources are sector-specfc. Factor markets are treated as perfectly compettve. Table 1: Commodtes Sectors and prmary factors n the general equlbrum model for Germany Prmary factors AGR Agrcultural goods CAP Captal MMC Basc materals / chemcal products LAB Labor EQP Investment goods RES Sector-specfc resource CSG Consumpton goods CST Constructon TRN Transport SER Prvate servces PUB Publc servces HCO Hard coal SCO Lgnte OIL Crude ol and refned ol products FOS Fossl fuels GAS Natural and manufactured gases ELE Electrcty and steam Producton Nested constant elastcty of substtuton (CES) cost functons are employed to specfy the substtuton possbltes n domestc producton between captal, labor, energy and materal (non-energy) ntermedate nputs. 3
Fgure 1 llustrates the nestng structure employed for producton sectors other than fossl fuels and electrcty. Output s produced wth fxed-coeffcent (Leontef) nputs of ntermedate non-energy goods and an aggregate of energy and a value added composte. The value-added composte conssts of a CES aggregaton of captal and labor. The energy aggregate s, n turn, produced wth a CES functon of electrcty and a composte of prmary energy nputs. The prmary energy composte s then defned as a CES functon of a CES aggregate of hard coal and lgnte and a CES aggregate of refned ol and natural gas. In the producton of electrcty, the prmary energy composte s defned as a CES functon of ol and an aggregate of coal and gas. The coal-gas composte s a CES functon of gas and a CES aggregate of hard coal and lgnte. In the producton of fossl fuels, labor, captal and fossl fuel nputs are aggregated n fxed proportons at the lower nest. At the top level, ths aggregate trades of wth the sector-specfc fossl fuel resource at a constant elastcty of substtuton. The latter s calbrated n consstency wth exogenously gven prce elastctes of fossl fuel supples. Output... Non-energy ntermedates Electrcty Captal Labor Hard Coal Lgnte Ol Gas Fgure 1: Structure of producton 4
The model allows for perfect as well as mperfect competton on good markets. Imperfect competton due to fxed costs s modeled as a Cournot olgopoly wth free market entry/ext,.e. each domestc ndustry conssts of dentcal frms, whose number s determned by the zero proft condton n conjuncton wth fxed costs and free market entry/ext (see secton 2.2 and Appendx B). Prvate demand, government and nvestment demand Prvate demand for goods and servces s derved from utlty maxmzaton of a representatve household subject to a budget constrant. Total ncome of the representatve household conssts of factor ncome and transfers. Utlty s derved from real consumpton and savngs. The top level of the utlty functon s specfed as a Cobb-Douglas functon resultng n a constant savngs rate. Real consumpton of the representatve agent s a CES composte of an energy aggregate and a Cobb-Douglas non-energy composte. The energy composte s defned as a CES functon of electrcty and the prmary energy composte. The prmary energy composte s gven as a CES functon of hard coal, lgnte and a CES aggregate of ol and gas. The structure of fnal demand s gven n Fgure 2. Government demand s fxed exogenously Total nvestment demand equals savngs; the nvestment good s a Cobb-Douglas aggregate of ntermedate nputs. Fnal Demand... Electrcty Non-energy goods Hard Coal Lgnte Fgure 2: Nestng structure for fnal demand Ol Gas 5
Internatonal trade All goods are traded nternatonally. Accordng to Armngton (1969), foregn trade modelng nvolves nternatonal product dfferentaton n the sense that mported and domestcally produced goods of the same knd are treated as ncomplete substtutes. For each product varety (Armngton aggregate) the substtuton possblty between the domestcally produced good and the world mport good s descrbed by a CES functon. The world mport goods, n turn, are gven as a CES aggregate of exports from Germany and exports from the rest of the world (ROW). The ROW closure requres that the value of mports to ROW are equal to the value of exports from ROW after ncludng a constant benchmark trade surplus (defct). Exports from ROW are determned by an export supply functon. An endogenous exchange rate assures that demand equals supply for ROW exports. 2.2 Market Structure Startng wth the semnal work by Krugman (1979), theoretcal and emprcal work n the feld of nternatonal trade has ncreasngly adopted scale economes and mperfect competton as a standard framework. By contrast, nternatonal aspects of envronmental polcy have mostly been examned under the more tradtonal assumptons of constant unt costs and perfect competton (see, e.g., Felder and Rutherford 1991, Pezzey 1992, Olvera- Martns, Burnaux and Martn 1992, Manne and Olvera-Martns 1994, Welsch 1996, Harrson and Rutherford 1997, Bernsten et al. 1999, Conrad and Schmdt 1998, Böhrnger 2000). Wthn the general framework descrbed n secton 2.1, each sector can delberately be modeled as beng perfectly or mperfectly compettve. Imperfect competton, f present, s due to fxed costs, not to regulaton of entry. In the presence of fxed costs; the number of frms s determned by the usual zero-proft condton. There are several ways n whch mperfect competton can be specfed. In the case of monopolstc competton (Krugman 1979), there are several ncompletely substtutable varetes of each good, and each frm n a partcular ndustry supples exactly one varety. Snce the elastcty of substtuton s the same for all pars of varetes, there s no dfferentaton between domestc and foregn supplers. In contrast to ths assumpton, we choose a set-up n whch varetes from the same country of orgn are closer substtutes for each other than are varetes from dfferent countres. Ths s n the sprt of Armngton (1969), who ntroduced the theory of demand for 6
goods dstngushed by place of producton. More specfcally, we assume that all domestc varetes are perfect substtutes for each other, as are all foregn varetes, but that domestc and foregn varetes are ncomplete substtutes. Ths specfcaton avods the dffculty of selectng ntra-country elastctes of substtuton; the nter-country (Armngton) elastctes are avalable from econometrc estmaton or lterature search (see Appendx C). In the presence of fxed costs, the chosen set-up mples that domestc supplers form a Cournot olgopoly. The market demand facng these supplers reflects the fact that domestc varetes compete wth ncompletely substtutable varetes from abroad. As usual n Cournot olgopoly, prces are a markup over margnal costs, where the markup rate reflects the number of frms and the elastcty of market demand (see Appendx B). Wth respect to the demand elastcty, t should be observed that market demand s the sum of several demand categores: ntermedate demand from the varous producton sectors, consumpton demand, nvestment demand, and export demand. The prce elastcty of market demand s the weghted average of the elastctes of the ndvdual demand categores, each weghted wth the correspondng value share. As envronmental taxes affect these shares, the elastcty of market demand s also affected, as are the markup rates. If the elastcty of market demand rses, the markup drops and frms are drven out of the market. As a consequence, economes of scale become effectve, and both unt costs and prces fall. The reverse happens f the value shares change n such a way that the overall demand elastcty gets reduced (see Fgure 3). Cost,Prce Margnal Cost P 0 P 1 Average Cost Markup 0 Markup 1 0 Y0 Y1 Fgure 3: Cost curves under mperfect competton due to fxed costs Output 7
2.3 Data and Parameterzaton Benchmark data are used to calbrate parameters of the functonal forms from a gven set of quanttes, prces and elastctes. Data from two dfferent sources are combned to yeld a consstent benchmark data set for 1995: EUROSTAT Input-Output-Table for Germany wth 25 sectors (Beutel 1999, EUROSTAT 1999). IEA energy balances and energy prces/taxes (IEA 1999). IEA provdes statstcs on physcal energy flows and energy prces for ndustral and household demands. The nformaton from IEA energy balances and energy prces s used to splt up the aggregate energy sector, as gven n EUROSTAT s nput-output table for Germany, nto the 5 energy sectors descrbed above. Our choce of elastctes s mostly based on revews of the relevant lterature (see, e.g. Burnaux et al. 1992). The Armngton elastctes between domestc output and mports have been estmated on tme seres data from the NEW CRONOS databank of EUROSTAT (for detals, see Böhrnger et al. 2000). Estmates of markup rates n varous ndustres can be found n Capros et al. (1997). These estmates suggest that, n terms of our sectoral classfcaton, mperfect competton can be taken to preval n the sectors 'basc materals and chemcals' (MMC) and 'nvestment goods' (EQP). The markup rates determne the share of fxed costs n total costs. Fxed costs are treated as part of captal costs. Appendx C provdes a summary of key elastctes and the markup rates employed for our smulatons. 3. Smulaton Results Our smulatons refer to a unform tax on carbon doxde that s unlaterally ntroduced n Germany to acheve the country's declared target of reducng ts carbon emssons untl 2005 by 25 percent as compared to 1990 emsson levels (Bundesregerung 2000). Snce BaU emssons n 2005 are projected to be 14 percent below 1990 levels (see European Commsson 1999), ths target mples an effectve abatement requrement of 11 percent below BaU. The revenue from the carbon tax s redstrbuted to prvate households n a lumpsum fashon. Smulatons have been performed under several assumptons concernng market structure. We contrast a scenaro n whch we assume perfect competton on all markets 8
(scenaro PC) wth a scenaro where the sectors MMC and EQP are mperfectly compettve (scenaro IC). The effects arsng n the latter scenaro are decomposed nto the contrbutons of each of the two mperfectly compettve sectors (scenaros IC_MMC and IC_EQP). 3.1 Macroeconomc Effects Table 2 shows the requred rate of the carbon tax and the nduced percentage changes n macroeconomc ndcators as compared to the benchmark level. In the case of all markets beng perfectly compettve (column PC) the tax rate s around 36 ECU per ton of CO 2. The reduced utlzaton of fossl fuels leads to a reducton of welfare (measured as Hcksan equvalent varaton HEV n ncome) by less than 0.1 percent and of GDP by one fourth percent. Wages and rental rates are almost 1.7 percent below BaU, ndcatng that reduced energy nput mples a consderable drop n factor productvty at the gven employment level. Table 2: Carbon tax and macroeconomc effects (percentage change) PC IC_MMC IC_EQP IC Welfare (HEV) -0.06-0.13-0.03-0.09 GDP -0.24-0.30-0.20-0.26 Consumpton -0.41-0.47-0.39-0.44 Investment 0.98 0.88 1.03 0.95 Wage rate -1.69-1.80-1.60-1.69 Rental rate -1.66-1.60-1.72-1.67 Exchange rate -0.90-0.83-0.92-0.85 Carbon tax* 35.64 35.20 35.66 35.20 * n ECU 95 per ton of CO 2 The total costs of carbon abatement under mperfect competton can be hgher or lower than those under perfect competton dependng on whether aggregate gans or losses n economes of scale across mperfectly compettve sectors preval. Under mperfect competton (IC), envronmental taxes have mplcatons for the number and sze of frms and, hence, for ther ablty to explot economes of scale. For reasons explaned below, carbon taxes reduce economes of scale n the MMC sector and hence exacerbate the "compettve" costs of carbon abatement. The reverse s true for mperfect competton n the EQP sector. On the whole - wth mperfect competton n both sectors - the macroeconomc effects of 9
carbon taxes for the German economy are slghtly more unfavorable compared to the compettve case because the negatve effect n the MMC sector domnates the postve effect n the EQP sector. 3.2 Sectoral Effects under Perfect Competton Even though the macroeconomc effects of carbon taxaton under mperfect competton do not dffer much from those under perfect competton, the effects on the sectoral level show a substantal dfference across the market structures. Consder frst the perfect competton case. As dsplayed n Table 3, the supplers of fossl fuels and the electrcty ndustry are facng a substantal declne n output. Other negatvely affected sectors are agrculture, basc materals and transport, all of them rather energy ntensve. On the other hand, consumpton goods, constructon, and prvate and publc servces experence a small ncrease; the nvestment goods ndustry has a rather sgnfcant expanson of output. The sectoral effects are determned by the varous ndustres factor ntenstes (see Appendx C). Especally, sectors wth a hgh energy/labor rato (EQP, CST, SER, PUB) are losers of structural change, whereas those wth a low energy/labor rato (AGR, FOS, ELE, MMC, TRN) beneft from the change n the rato of wages to energy costs. These relatonshps are consstent wth standard factor endowment models n whch emssons represent the factor nput "envronment": The mposton of an envronmental tax on emssons ncreases the prce of the factor "envronment". Consequently, less of ths factor wll be used. The producton of the "drty" goods, whch use the envronment ntensvely, wll therefore decrease, and that of the envronmentally frendly,.e., captal/labor ntensve good wll ncrease. Prevous smulaton studes n perfect competton settngs have typcally been n lne wth ths logc and produced results very smlar to ours: Basc ndustres of outward orented economes experence losses, whereas other manufacturng sectors tend to gan. 2 On the nternatonal level, these changes n the cost structure translate nto changes n comparatve advantage. As shown n Table 4, any ncrease (or decrease) n output goes along wth an ncrease (decrease) n exports. Note that the changes n exports are more pronounced than the correspondng changes n output. For nstance, exports of nvestment goods rse by 3 percent, whereas total output ncreases not more than 1.4 percent. Exports of basc materals and chemcals, conversely, drop by almost 10 percent, whereas output drops by only about 3.6 2 For a revew of the standard (perfect competton) factor endowment approach to envronmental taxes, producton and trade as well as of smulaton results obtaned n ths framework see Klepper (1998). 10
percent. The reason for these results s that the prce elastcty of export demand s larger than the prce elastcty of the varous categores of domestc demand. Table 3: Change n output (percentage change) PC IC_MMC IC_EQP IC AGR -0.56-0.49-0.61-0.56 FOS -14.17-14.14-14.18-14.15 ELE -6.89-7.05-6.88-7.05 MMC -3.64-5.19-3.77-5.45 EQP 1.36 1.60 1.69 2.06 CSG 0.13 0.22 0.07 0.14 CST 0.35 0.31 0.35 0.31 TRN -4.19-4.03-4.35-4.23 SER 0.08 0.03 0.11 0.06 PUB 0.03 0.02 0.03 0.01 Table 4: Change n exports (percentage change) PC IC_MMC IC_EQP IC AGR -4.47-4.02-4.68-4.31 FOS -29.21-28.93-29.28-29.01 ELE -46.40-45.56-46.53-45.70 MMC -9.69-13.69-10.15-14.54 EQP 3.01 3.78 3.71 4.78 CSG 0.42 1.10 0.02 0.59 CST 2.18 3.25 1.58 2.49 TRN -14.68-13.11-15.46-14.04 SER 6.62 7.73 6.27 7.27 PUB 6.99 8.92 5.89 7.58 3.3 Sectoral Effects under Imperfect Competton Wth respect to the structure of trade, envronmental taxes lead to a change n comparatve advantage. Ths s true rrespectve of the market structure. Under mperfect competton, however, the change n comparatve advantage has mplcatons for market structure: Wth free entry and ext, the number of frms n a partcular ndustry s nversely related to the prce 11
elastcty of market demand. A gan n an ndustry s comparatve advantage leads to a shft n sales from the domestc markets to the export markets. Gven that the prce elastcty of export demand s larger than the prce elastcty of domestc demand, ths mples a rsng overall prce elastcty, wth an ncrease n scale economes. The reverse happens f an ndustry faces a loss n comparatve advantage. These effects are llustrated n Table 5 and Table 6. If mperfect competton s restrcted to the basc materals/chemcals ndustry (IC_MMC), the overall demand elastcty of ths sector reduces by more than 6.5 percent, and economes of scale (defned as output per frm) drop by almost 7 percent. In the case of the nvestment goods ndustry beng mperfectly compettve (IC_EQP), both ts demand elastcty and scale economes rse by about 1.3 percent. In our core scenaro, n whch both of these ndustres are mperfectly compettve, scale economes drop by almost 7.3 percent n the basc materals/chemcals ndustry, whle rsng by 1.7 percent n the nvestment goods sector. Table 5: Change n demand elastctes (percentage change) PC IC_MMC IC_EQP IC MMC - -6.55 - -7.05 EQP - - 1.35 1.82 Table 6: Change n economes of scale (percentage change) PC IC_MMC IC_EQP IC MMC - -6.83 - -7.27 EQP - - 1.26 1.72 The nduced changes n economes of scale mply that structural change s more pronounced under mperfect competton than under perfect competton. As shown n Table 3, the drop of basc materals/chemcals output s 50 percent larger f the basc materals/chemcals and nvestment goods ndustres are mperfectly compettve than t s n the perfect compettve case. Conversely, the ncrease of nvestment goods output s substantally enhanced f these two ndustres are characterzed by mperfect competton. The effects at the sectoral level explan the macroeconomc outcome descrbed above (see secton 3.1): Rsng scale economes n the nvestment goods ndustry would mply that the losses n welfare and GDP declne, relatve to the perfect competton case, whereas decreasng scale economes n the basc materals/chemcals ndustry enhance these losses 12
(see Table 3.1, columns IC_EQP and IC_MMC). If both sectors are mperfectly compettve (column IC), the nduced effcency losses n basc materals/chemcals domnate the effcency gans n nvestment goods, and the welfare loss s larger than t s n the perfect compettve case. 4. Conclusons In ths paper we analyzed how the economc effects of envronmental taxes depend on the underlyng market structure. Under mperfect competton wth free entry and ext, envronmental taxes have an mpact on economes of scale by changng the number and sze of frms. Whether economes of scale rse or fall n a partcular ndustry depends on nduced changes n the prce elastcty of demand. Because export demand s more prce elastc than domestc demand, the overall prce elastcty rses (falls) as the ndustry gans (loses) n comparatve advantage. We used a computable general equlbrum model for Germany to contrast the effects of a unlaterally ntroduced carbon tax under perfect vs-a-vs mperfect competton. Irrespectve of the market structure, envronmental taxes lead to a change n comparatve advantage - ndustres wth a hgh energy/labor rato lose and ndustres wth a low energy/labor rato gan. Under mperfect competton, these changes have drect consequences on the economes of scale n mperfectly compettve sectors. In the case examned, the nvestment goods ndustry (EQP) gans a comparatve advantage and, hence, n economes of scale whereas the reverse apples to the basc materal/chemcals ndustry (MMC). Therefore, the structural change nduced by carbon taxes s more pronounced under mperfect competton as compared to perfect competton. At the macroeconomc level, the total costs of carbon abatement under mperfect competton can be ether hgher or lower than those under perfect competton, dependng on whether aggregate gans or losses n economes of scale across mperfectly compettve sectors preval. In our smulatons for Germany, the loss n economes of scale wthn MMC domnates the gans wthn EQP; on the whole the total costs of carbon abatement turn out slghtly hgher than under perfect competton. 13
The mpact of mperfect competton on the structural change nduced by envronmental taxes has so far been lttle explored. Gven that mperfect competton prevals n varous goods markets, our fndngs suggest that the structural mpacts of envronmental taxes may be larger than prevously assumed. 14
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Appendx A. Algebrac Model Summary Ths appendx provdes an algebrac summary of the equlbrum condtons for the generc comparatve-statc model wth perfectly compettve markets (see Appendx B for the extenson wth respect to the specfcaton of mperfectly compettve good markets). Two classes of condtons characterze the compettve equlbrum: zero proft condtons and market clearance condtons. The former class determnes actvty levels and the latter determnes prce levels. In our algebrac exposton, the notaton z Π s used to denote the proft functon of sector where z s the name assgned to the assocated producton actvty. Dfferentatng the proft functon wth respect to nput and output prces provdes compensated demand and supply coeffcents (Shephard s lemma) that appear subsequently n the market clearance condtons. Table A1 explans the notatons for varables and parameters. Key elastctes are summarzed n Table A2. Estmated Armngton elastctes are gven n Table A3. Table A4 gves sectoral benchmark captal and energy ntenstes. Sectoral markup rates are summarzed n Table A5. For the sake of transparency, we do not wrte down the explct functonal forms but nstead use the acronyms CET (constant elastcty of transformaton), CES (constant elastcty of substtuton), CD (Cobb-Douglas) and LT (Leontef) to ndcate the class of functonal form n place. Zero Proft Condtons Aggregate output: ( ) Y (A.1) P LT PA CES PE CES ( PL PK) Π = n, n N,,, = 0 ( ) Y Π = P CES PR, LT PL, PK, PA j = 0 V F Energy aggregaton: ( ) E (A.2) PE CES PA CES CES ( PA PA ) CES ( PA PA ) Π = - ELE, HCO, SCO, GAS, OIL = 0 ( ( ( ))) E Π = PE- CES PAELE, CES PAOIL, CES PAGAS, CES PAHCO, PA SCO = 0 I \ ELE = ELE 18
Armngton aggregaton: Π = PA - CES P, PM P a = 0 (A.3) A 2 2 ( ) CO CO World mport good producton: M (A.4) Π ( ) Utlty producton: = PM - CES PA, PFX = 0 U (A.5) PU CD ( PC PINV ) Investment: Π = -, = 0 INV (A.6) Π ( I) Fnal demand: = PINV - LT PA =, 0 ( ) C (A.7) PC CES CES ( PAn, n N ) CES PAELE CES ( PAHCO PASCO CES ( PAOIL PAGAS )) Π = -,,,,, = 0 Market Clearance Condtons Labor: (A.8) L = Y Y Π PL Captal: (A.9) Π Y K = Y PK Natural resources: (A.10) Q f = Y f Y Π f PR f Domestc output: (A.11) Y=A Π P A 19
Energy aggregate: (A.12) Π Y E = Y PE World mport good: (A.13) Π M A M A ROW = + PM Armngton aggregate: (A.14) Π A Y C INV M Y C INV M j Π Π Π = j + + + j PA PA PA PA Prvate demand: (A.15) U Π C = U PC Investment: (A.16) U Π INV = U PINV Carbon emssons: (A.17) ROW closure: CO 2 = A a CO2 (A.18) ROW σ M INC PM PM θ = PFX + B PFX PFX ROW M ROW INC Foregn closure (PFX): (A.19) σ PM M = PFX M Π PFX M 20
Table A1: Sets, actvty and prce varables, endowments Sets: I,, j Sectors and goods (13 commodtes) E, e Energy goods (HCO, SCO, OIL, GAS and ELE) N, n Non energy goods F, f Fossl fuels (HCO, SCO, GAS) V, v Non fossl fuels Actvty varables: Y Aggregate producton E Aggregate energy nput A Armngton aggregate M World mport aggregate ROW M ROW mport demand U Household utlty INV Aggregate nvestment C Prvate consumpton Prce varables: P Output prce PE Prce of aggregate energy PA Prce of Armngton aggregate PM Prce of world mport aggregate PFX ROW export and mport prce PU Utlty prce ndex PC Prce of aggregate household consumpton PINV Prce of nvestment demand PL Wage rate PK Prce of captal servces PQ f Rent from natural resource P CO2 Prce of carbon permt Endowments: L Aggregate labor endowment K Aggregate captal endowment Q f B Endowment of natural resource f Balance of payment surplus CO2 Endowment wth carbon emsson rghts Other parameters: CO2 a θ σ M Carbon coeffcent Expendture share of world mport good ROW export supply elastcty 21
B. Specfcaton of Imperfect Competton Each mperfect compettve sector j s modeled as a homogenous Cournot-Olgopoly. The output prce (P j ) s then gven as markup on margnal cost (MC j ): (B.1) MC j Pj = 1 1 N η j j, where η j s the prce elastcty of market demand and N j the number of frms n the sector. Because of free market entry, the zero proft condton holds,. e. the number of frms changes n such a way that output prce equals average cost. The elastcty of market demand s consstng of the substtuton elastctes and value shares of the dfferent market stages. If several goods Z 1,...,Z N form an aggregate Z, the prce elastcty of good n (1,...,N) s: (B.2) η = σ ( 1 θ ) n n where σ s the elastcty of substtuton between the dfferent goods and θ n s the value share of good n, gven that the level of the aggregate Z s seen as exogenous. If Z s n contrast a sub-aggregate n an aggregaton herarchy, one has to consder the prce elastcty of Z, whch depends n the same manner on the substtuton elastctes and value shares of hgher stages. Ths logc contnues untl a stage s reached that s no longer prce dependent from the vew of the agents. In our market herarchy, there are two of these stages. Domestc output Y of the good competes wth mports M of the world mport good. Both form the Armngton aggregate A, whereby the Armngton substtuton elastcty s denoted as σ A and the value share of the domestc output as s Y,A. A porton s D of the Armngton good goes to the domestc market wth the prce elastcty η D, whereas a porton s M s sold on the export market (formng the world mport good M ) wth a prce elastcty of η M. The prce elastcty on the export market depends on the substtuton elastcty between exports from Germany and ROW exports n the producton of the world mport good σ M and the value share of the German Armngton good exports n the world mport composte s EX,M. The level of the world mport aggregate s seen as exogenous by German frms. The demand elastcty for Y wth regard to the prce P s then gven as: 22
(B.3) ηyp, = σ A (1 sya, ) + sd ηd+ sm σm ( sya, (1 sexm, )) Important s the last term of equaton B.3, whch s related to the competton on the world market. Snce the elastcty of substtuton on the world market σ M s hgher than the substtuton elastcty on the domestc market σ A, an ncreased (decreased) share of exports n total output results n a hgher (lower) prce elastcty of the good and a lower (hgher) markup on margnal cost. Increasng export orentaton thus reduces market power. C. Summary of Key Elastctes and Markup Rates Table C1: Selected substtuton elastctes Producton Captal-labor-energy vs. ntermedates 0 Captal-labor vs. energy 0.6 Captal vs. labor 0.8 Electrcty vs. prmary energy nputs 0.3 Hard coal and lgnte vs. gas and ol 0.5 Hard coal vs. lgnte 2 Gas vs. ol 2 Hard coal, lgnte and gas vs. ol n electrcty producton 0.5 Hard coal and lgnte vs. gas n electrcty producton 2 Hard coal vs. lgnte n electrcty producton 3 Consumpton Energy goods vs. non-energy goods 0.5 Electrcty vs. prmary energy nputs 0.5 Hard coal and lgnte vs. ol and gas 0.2 Ol vs. gas 0.3 Non-energy goods vs. non-energy goods 1 Trade Armngton goods and ROW exports n world mport good 16 23
Table C2: Estmated Armngton elastctes for Germany (1979-1991)* Sector Armngton Elastcty t-value MMC Basc materals / chemcal products 2.039 6.908 EQP Investment goods 2.325 3.669 * Armngton elastctes for all other sectors are set equal to 2. Table C3: Sectoral benchmark captal and energy ntenstes Labor ntensty Energy ntensty Energy/labor rato HCO 0.38 0.26 0.67 SCO 0.06 0.44 7.54 OIL 0.07 0.59 8.03 GAS 0.13 0.13 0.97 ELE 0.16 0.26 1.69 AGR 0.14 0.07 0.49 MMC 0.20 0.08 0.42 EQP 0.28 0.02 0.06 TRN 0.48 0.07 0.15 CSG 0.21 0.03 0.13 CST 0.36 0.02 0.07 SER 0.21 0.01 0.05 PUB 0.57 0.01 0.02 Table C4: Sectoral markup rates* Markup rate MMC 5.2 EQP 7.1 * based on Capros et al. (1997) 24