Emission Abatement with Per Capita and Trade Considerations

Transcription

1 Emsson Abatement wth Per Capta and Trade Consderatons Amnon Levy School of Economcs Unversty of Wollongong and Jonathan Lvermore Department of Agrculture, Food and atural Resources Unversty of Sydney Abstract In the absence of a comprehensve nternatonal agreement, each country unlaterally sets her abatement of greenhouse gas emssons at a level that possbly maxmzes her ected net beneft. In addton to a cleaner and healther domestc envronment and a slower global warmng, a country s beneft from self emsson-abatement may nclude mproved mage and, n turn, blateral economc and poltcal relatons. Ths paper analyses a country s cooperatve and non-cooperatve emsson abatements wthn a cost-beneft framework that, for equalty consderaton, s centered on per capta emsson and takes nternatonal rewards for commtment to be responsve to per capta ncome and output composton.

2 . Introducton Prevous studes have consdered the effect of nternatonal economc relatons, partcularly trade, on greenhouse gas emssons. For example, Barrett (997 has study the role of trade sanctons n deterrng free rdng. Usng a general equlbrum model wth a game theoretc component, Alpay (000 has shown under whch condtons trade can stmulate envronmental protecton. Eyckmans and Tulkens (003 have ntroduced a world model for smulatng cooperatve game theoretc aspects of global clmate negotatons. Most relevant to our study, Kemfert, Lse and Tol (004 have focused on the queston how nternatonal trade changes optmal emsson-reducton and ncentves to cooperate on emsson-reducton. Ther modellng of a country s cost of emsson-reducton has attempted to capture the domestc costs of self emsson-reducton, the effect of nternatonal varaton n the level of strngency of emsson-reducton polcy on the country s terms of trade and captal flow, and the negatve external effect on the country s ort of a slowng nternatonal economc growth due to foregn emsson reducton. The models used n these studes focus on aggregate levels of domestc and foregn emssons and some of ther assumptons hold only f the countres were dentcal. Countres dffer n populaton sze, technology, ndustral structure, ort of emsson-ntensve manufactured goods, and consumpton level and pattern. Although Chna, and to a lesser extent Inda, contrbutes about thrty percents of the global atmospherc greenhouse gas emssons, the per capta emssons of ths maor workshop of hghly affordable, tradable, manufactured goods are about one ffth of Australa (the world s number one, the Unted States and Canada. These dfferences and equty are not captured by models focusng on countres aggregate levels of emssons. The cost-beneft model presented n the followng sectons s centered on per capta emsson reducton. Per capta ncome and output composton nfluence the assessment of, and reacton to, a country s commtment to emsson abatement by other countres. Ths nfluence s ncorporated nto the determnaton of the nternatonally cooperatve and non-cooperatve emsson reductons. The analyss reveals that when ths nfluence s taken nto account the non-cooperatve emsson For nstance, n Kemfert, Lse and Tol (004 there s no external cost effect on a country va the terms of trade and nternatonal captal dynamcs when all the countres abate the same level of emssons (.e., g ( R R = 0 when R = R.

3 reducton by some countres may exceed ther optmal nternatonally cooperatve abatement.. A country s costs and benefts of abatement The total cost for country of reducng ts per capta greenhouse gas emssons from the present perodcal level e to e ncludes the full costs of enforcement of, and ˆ adaptaton to, the new lower domestc emsson level. We assume that these mtgaton and adaptaton costs (MAC convexly rse wth the country s aggregate emsson-abatement level: MAC = c [ e P ] ( where P denotes country s populaton and c s a postve scalar ndcatng the gradent of country s margnal abatement costs. We further assume that the margnal cost gradent declnes from a maxmal level wth the country s level of development as some producton and consumpton actvtes are less panfully foregone and as technologcal absorptve and nnovatve capactes are mproved. Takng per capta ncome ( gven by: c c > 0 y as reflectng level of development, we let c/ y. ( = A reducton of domestc emssons ncreases the health and recreatonal value of country s envronment for resdents and foregn toursts. Due to transboundary externaltes, ths domestc envronment s apprecaton ( DEA also depends on the c be emssons abated by other countres. We take DEA to be lnear (for tractablty n country s emsson-abatement, counterpart s emssons abatement, e P, and n each of her ( =,,3,..., e P. The average external effect of any country s emsson-abatement on DEA depends on the drectonal algnment of and wth domnant wnds, on the dstance between and and on the structure of the surface separatng from. Due to these ntervenng factors, the average external effect ( β 0 s lkely to be smaller than the average nternal effect ( α > 0 of s emsson abatement. Wth e denotng country s ectatons about any country s per capta emssons, country s ected domestc envronment s apprecaton s: 3

4 = α ˆ + β ˆ EDEA ( ( e e P ( e e P. (3 EMGW ( = γ e P + e P. (4 By reducng her emssons, country also contrbutes to the aggregate nternatonal effort of moderatng the global accumulaton of greenhouse gases and, n turn, global warmng. We take country s ected beneft (n nomnal unts from a moderated global warmng (MGW to be gven by: where γ s a postve scalar ndcatng a fxed (for tractablty margnal beneft to country from the aggregate effort to moderate global warmng. As other countres envronment and terms of trade depend on country s commtment to emsson reducton, there are nternatonal benefts to country from mpressng her counterparts of beng envronmentally responsble and nonopportunstc tradng partner. Yet country cannot equally mpress all her counterparts. A less commtted country may regard country as an envronmentally responsble and non-opportunstc tradng partner, whereas a more commtted country may deem country an envronmentally rresponsble and opportunstc tradng partner. Hence, country may economcally and poltcally be rewarded by the former, but sanctoned by the latter. As a hgher degree of tolerance s lkely revealed toward a low-ncome country producng tradable goods, the sanctons and rewards may be responsve to the porton of the per capta ncome generated by ort orented ndustres. We therefore assume that country ects her economc and poltcal relatons wth any other country to change wth the relatve strngency of ther non-ort ncome deflated emsson-abatement polces. More specfcally, we assume that country ects the loss (n nomnal unts of relatons wth country to dmnsh from a maxmal level LR max 0 wth her rato of per capta abatement to per capta non-ort ncome, relatve to that of country. The maxmal loss depends on the nature of the ntal relatons, relatve sze and nternatonal nfluence of and. Consequently, country s ected aggregate loss of nternatonal relatons (ALIR s: EALIR ( LR r max ( e e/ sy = e / sy ˆ. (5 4

5 The scalar 0 denotes country s non-ort ncome share. The scalars s r 0 and / /[ e s y ] 0 ndcate, respectvely, country s percepton of country s ablty and nclnaton to reward country s commtment to per capta domestc emsson-reducton wth more favorable economc and poltcal relatons. A negatve (postve ( EALIR reflects country s overall ectaton to be rewarded (sanctoned for her relatvely strong (weak commtment to emsson abatement wth hgher (lower level of economc and poltcal nternatonal cooperaton. In vew of these costs and ected benefts, country s ected net beneft ( EB from reducng her greenhouse-gas emssons s: EB = E( DEA + E( MGW E( ALIR MAC e P e P = ( α + γ ( + ( β + γ ( + ˆ max e e LR r ( s y / s y ( c / y ( ˆ e e P e. (6 3. Optmal emsson abatement: cooperatve vs-à-vs non-cooperatve The cooperatvely optmal abatement of per capta emssons by country s o = arg max = e EB ( c/ y P > /[ r ( s y / s y e / e. As long as 3, EB s concave n e and the margnal ected global beneft from country s optmal per capta emsson reducton s equal to ths country s margnal cost of the optmal per capta emsson abatement: r ( / s y s y ( α + γ P + + P ( o β + γ e = o o ( / ( ˆ ( / ( ˆ o r s y s y e e = c y e e P e Country s cooperatvely optmal abatement rses wth her own and counterparts margnal benefts from mproved domestc envronments and moderated global warmng and wth her mproved nternatonal relatons, but dmnshes wth the.(7 5

6 eroson of her counterparts relatve abatement and subsequent blateral relatons wth her. It also decreases wth the gradent of country s margnal costs of abatement. Though not a close-form soluton of equaton (7, t s useful for a comparson wth the non-cooperatve emsson abatement to ress country s cooperatvely optmal per capta emsson abatement as: o e = o ( / (ˆ ( / r s y s y e e r s y s y + P + + P o + o e e ( c/ y P ( α γ ( β γ.(8 In the absence of cooperaton, each country maxmzes her ndvdual ected net beneft from emsson abatement. As nteror e = arg max EB EB from abatement to her margnal cost of abatement: r ( s y / s y ( α ( / ( + γ P + = c y ˆ e e P e s concave n e, there exsts an. It equates country s margnal ected self beneft Consequently, for every country =,,3,..., the non-cooperatve ected net. (9 beneft maxmzng abatement of per capta emssons s equal to the rato of the sum of her own margnal benefts from the mprovements n her domestc envronment, global envronment and nternatonal relatons to the gradent of her margnal costs of abatement: r ( s y / s y ( α + γ P + e = ( c/ y P. (0 e Suppose that s a large manufacturng country of hghly affordable, tradable goods. If the rest of the countres are ected, despte beng less ntensve workshops of affordable and tradable goods, to be weakly commtted to emsson-abatement, ther aggregate ablty and nclnaton to reward country ( r /[ e / s y ] s perceved by country to be low. Consequently, the per capta emssons abated by country s manly determned by her domestc and global envronmental self nterests and s smaller than the cooperatvely optmal level. Moreover, selfshness mght lead to power abuse. A large producer of hghly affordable and ortable 6

7 goods, who s also capable of nflctng a large punshment max LR on any other country and who strongly evaluates her own beneft from mproved global envronment (.e., has a large γ, mght coerce other countres nto abatng greater quanttes of emssons than the cooperatvely optmal ones by adherng to an nflexble puntve polcy (low r. The possblty that for some countres the noncooperatve ected net beneft maxmzng abatement of per capta emssons s larger than the cooperatvely optmal level s ndcated n the followng proposton. PROPOSITIO: If P ( β + γ + r ( s / s y y e o ( s y / s y ( / ( > o + o r s y s y e < e e = r < o then { e } = { e }. (Straghtforward from equatons (8 and (0. > 4. Cournot-ash equlbrum and concludng remarks If each country s ectatons about the other countres abatement levels are perfect e ( e =, the soluton of the equaton-system (0 s the Cournot-ash equlbrum of the countres emsson-abatement levels. In order to shed lght on the propertes of the Cournot-ash equlbrum levels of abatement, the analytcally tractable case of a world dvded nto two allances s consdered (e.g., an allance of poor workshop countres of tradable prmary and manufactured goods versus the rest of the world. In ths case, the ected-net-beneft maxmzng per capta emssons are r s y y ( / s ( α + γ P+ e ( c/ y P e = ( for allance, and by symmetry, e r ( s y / s y ( α + γ P + e = ( c/ y P. ( 7

8 for allance. The soluton to ths system of reacton equatons yelds the Cournot- ash equlbrum per capta emsson-abatement for allance : α+ γ α+ γpp + c yrs ˆ s y sy P c yr sy syp e e = 0.5 ( c/ y( α + γ PP [0.5( ( ( / ( / ( / ( / ] 0.5( α+ γ( α+ γ PP + ( c/ y r( sy/ sy P ( c/ y r( sy/ sy P ( α+ γ Pr ( sy/ sy ( c/ y( α + γ PP ( c/ y( α + γ PP.(3 The quantty and propertes of ˆ (e e are obtaned by symmetry. Equaton (3 reveals that n a Cournot-ash equlbrum, the per capta emsson abated by allance ˆ (e e rses wth the margnal mprovement n ts own envronment generated by ts own abatement ( α, wth ts margnal beneft from the combned effort of curbng global warmng ( γ, wth allance s ablty to reward commtment weghted by ts relatve non-ort per capta ncome ( r ( s y / s y and wth allance s margnal abatement costs gradent ( c / = c y. In the Cournot- ash equlbrum, allance s per capta emsson-abatement declnes wth ts own margnal abatement costs gradent ( c = c/ y and wth the sze of ts own populaton P (. In order to assess the effect of allance s ablty to reward allance and the effect of allance s populaton sze on allance s emsson-abatement level n a Cournot-ash equlbrum note that e 0.5 = 0.5[/(( α + γ P]{ + [ ( α+ γ /(( c/ y P ] Δ } (4 { r [( s y /( s y ]} and e = 0.5[(( c/ y r( y/ y /(( c/ y( α + γ P + ( r( sy/ sy /(( α + γ P ] P where Δ>0 0.5 c y r sy sy c y α γ P c y P r sy sy P Δ {(( / ( / /(( / ( + + [ ( α + γ /(( / ][ ( / /(( α + γ ]} (5 s the dscrmnant (the square of the second term on the rght hand sde of equaton (3. As long as the populaton of allance ( γ P s not very small [ ( α + /(( c/ y P] > 0. In whch case, the per capta emssons abated by 8

9 allance n a Cournot-ash equlbrum rse wth the populaton of allance and declne wth allance s ablty to reward allance (. The emsson-abatement moderatng effect of the latter factor s ncreased by allance s relatve non-ort per capta ncome ( sy / sy. Recallng that r ˆ ( e e / { r [( s y /( s y ]} > 0, the total effect of allance s relatve non-ort per capta ncome allance s emsson reducton s negatve. ( sy/ s y on 9

10 Appendx: The Cournot-ash equlbrum Recall (, ( and (, r( s y / s y ( α+ γ P+ e e = (A cp and r( s y / s y ( α + γ P + e e =. (A cp Let θ α+ γ, θ α + γ, y = sy and y = sy and substtute the rght hand sde of A nto A: r( y / y θp+ r( y / y θp + e cp e = cp (A3 In turn, cp r( y / y (ˆ e e cp e θp = (A4 θp e + r( y / y By rearrangng terms, θ PcP e [ θθ PP + cp r( y / y cr ( y / y P ] e (A5 θpr ( y / y = 0 and, consequently, [0.5 θθ PP + cr( y / y P cr ( y / y P ] θpr ( y / y e e = cθpp cθp P (A6 The roots of (A6 are: [0.5 θθ PP + cr( y / y P cr ( y / y P ] e = 0.5 cθ P P PP + cr y y P c r y y P θ r y y cθpp cθpp 0.5 θθ ( / ( / ( / ± (A7 As the dscrmnant n (A7 s postve and larger than the absolute value of the coeffcent of (e e n (A6, only the followng root s consdered to be relevant: ˆ θθ PP + cr y y P cr y y P e = cθ PP [0.5 ( / ( / ] 0.5 PP + cr y y P c r y y P θ r y y cθpp cθpp 0.5 θθ ( / ( / ( / (A8 0

11 References Alpay, S. (000, Does Trade Always Harm the Global Envronment? A Case for Postve Interacton, Oxford Economc Papers 5(, Barrett, S. (997, The Strategy of Trade Sanctons n Internatonal Envronmental Agreements, Resource and Energy Economcs 9, Eyckmans, J. and Tulkens, H. (003, Smulatng Coaltonally Stable Burden Sharng Agreements for the Clmate Change Problem, Resource and Energy Economcs, 5 (4, Kemfert, C.; Lse, W. and Tol, R. S. J. (004, Games of Clmate Change wth Internatonal Trade, Envronmental and Resource Economcs 8 (, 09-3.