Optimal Commodity Taxation under International Positional and Environmental Externalities

Transcription

1 Optmal ommodty Taxaton under Internatonal ostonal and Envronmental Externaltes Fe Ao Fe Ao Sprng Semester 2017 Master Thess, 15 ETS Master s rogram n Economcs

2 Abstract The facts that relatve consumpton concerns may gve rse both to postonal and envronmental externaltes, and that these two externaltes are ncreasngly transboundary requre us to derve an optmal commodty tax n an nternatonal framewor. The correctve tax polcy decded at a natonal level s found to fal to nternalze all postonal and envronmental externaltes. The optmal tax polcy under an nternatonal cooperatve framewor reflects correcton for both global postonal and envronmental externaltes. In ths broader framewor, we also characterze the provson of polluton abatement as an addtonal polcy nstrument. The results show that relatve concerns for one of the prvate goods do not lead to any modfcaton of the polcy rule for publc abatement. Key words: Optmal taxaton, elatve consumpton, ostonal goods, ostonal and envronmental externaltes, areto optmal allocaton, Internatonal cooperatve framewor

3 1. Introducton 1.1 Bacground A postonal good s defned by Hrsch (1976) as a good where the utlty derved from t reles negatvely on ts consumpton by others. The competton for a postonal good s then featured by a zero-sum game. A postonal externalty occurs when new purchases alter the relevant context wthn whch an exstng postonal good s evaluated (Fran 2008, 1777), whch mples that ncreased consumpton by a partcular ndvdual leads to lower utlty for other people. Fran (1997) argues that ths relatve consumpton concern s harmful to socety as a whole. Taxaton of postonal goods s needed to prevent overconsumpton to avod socal waste. In addton, f postonal concerns lead to overconsumpton of the good n queston, and f ths good also gves rse to envronmental externaltes, t follows that postonal concerns may renforce the envronmental externalty. For example, besdes straghtforward satsfacton the consumpton of a hghly postonal commodty le a car can brng to consumers, compared to those who have more luxurous or cheaper cars, the consumer feels dsapponted or happy, whch can be descrbed as relatve deprvaton, envy, jealousy or nequty. If postonal concerns lead the ndvdual to drve more to sgnal status by showng the expensve car, ths wll lead to ncreased envronmental damage. The envronmental externaltes wll n addton negatvely affect each person ncludng the car s owner. Generally, the benefcares and vctms of polluton do not voluntarly transact for the socety to realze an effcent allocaton. The pursut of a hgher socal status may lead to overconsumpton and welfare costs both n terms of postonal and envronmental externaltes (Ng and Wang, 1993). Therefore government nterventons, such as a correctve tax, publc good provson, etc., are needed to crcumvent the potental welfare costs; for nstance, Howarth (1996) shows that consumpton taxes are necessary to offset ncentves to overconsume at the expense of envronmental qualty. At least two facts suggest that we ought to examne the externalty correctng tax polcy n an nternatonal framewor. Frstly, the rapd spread of nformaton fostered by globalzaton maes t possble that socal comparsons go beyond natonal borders. 1

4 Easer access to T, Internet, and socal meda together wth ncreased travellng facltate havng a better nowledge of others ncludng celebrtes, commercal eltes, etc. Ths suggests that people s reference consumpton s ncrementally nfluenced by consumpton levels n other countres. Secondly, the ntegrty of the global natural envronment necesstates an nternatonal analyss framewor. The envronmental damage generated n each country typcally splls over to other countres. Therefore, correctve taxaton decded at the natonal level does not n general nternalze all externaltes. 1.2 General purpose and motvaton The man purpose s to derve an optmal commodty tax n a framewor where the consumpton of a partcular good generates postonal and envronmental externaltes, and where these two externaltes are transboundary. To ths end, a statc game model wll be used. In the model, each consumer s assumed to maxmze utlty, through an optmal allocaton n prvate consumpton between postonal and non-postonal commodtes, subject to hs or her budget constrant. The polcy maers are assumed to choose a commodty tax polcy to maxmze a socal welfare functon subject to a publc sector budget constrant. In dong so, we start wth an analyss of the tax polcy outcome of noncooperatve behavor, such as Nash and Stacelberg competton, between countres. These allocatons are not globally effcent, snce non-cooperatve behavor s based on a natonal polcy objectve, meanng that the correctve taxes decded at the natonal level may not reflect the welfare costs that domestc resdents mpose on people n other countres. Note that ths argument also apples to Stacelberg competton, despte that the leader n the Stacelberg game consders the followers consumpton reacton functons. Then we focus on cooperatve behavor, where a global socal planner can tae nternatonal postonal and envronmental externaltes nto consderaton when characterzng the optmal commodty tax for the whole global economy. Wthn ths nternatonal cooperatve framewor, t s also nterestng to characterze the polcy rule for publc abatement expendture, whch exemplfes contrbuton to a publc good. The socal planner needs to decde how much resources should be transferred from prvate consumpton to publc good provson. The results show that the polcy rule for publc good provson taes the same general form as n the absence of any postonal concerns. Therefore, our result dffers from those of Aronsson and Johansson-Stenman (2014), who found that relatve consumpton concerns tend to modfy the polcy rule for publc good provson, as long as ths rule s based on the sum of the ndvduals prvate margnal 2

5 wllngness to pay for the publc good. The reason for ths dscrepancy s that we dstngush between dfferent prvate consumpton goods where only one of them generates externaltes, whereas Aronsson and Johansson-Stenman (2014) assumed that all prvate consumpton s subject to postonal concerns. There are few emprcal studes drectly related to the topc of the present paper, whle many emprcal studes address three aspects partally related to t. Frstly, socal status comparsons play an mportant role n ndvdual s well-beng. The comparsons examned n earler studes refer to ncome and consumpton. Easterln (1974) concludes that both absolute and relatve consumpton are mportant determnants of lfe-satsfacton at the ndvdual level. Bree and Howarth (2002) conclude that about one-thrd of consumpton satsfacton s determned by postonal consderatons. Ths weght s 20-40% n Wendner and Goulder (2008). Solnc and Hemenway (1997) use a questonnare expermental approach to show that respondents would even accept a 50% decrease n absolute ncome as long as relatve ncome s hgher compared to the other members of socety and thus eep a hgher socal status. Luttmer (2005) shows that ndvduals selfreported happness s negatvely affected by the earnngs of others n ther area of resdence. Increased neghbors earnngs have a strong negatve effect on happness for those who have a broader socal networ. lar and Sen (2010) carry out an extensve nvestgaton about ncome comparson effects n Europe. They dscuss dfferent ncome comparson groups, le wor colleagues, famly members, frends, etc. as well as analyze the ntensty and drecton of ncome comparsons to estmate the extent to whch such comparsons matter. Ther results suggest that colleagues consttute the most mportant reference group. Secondly, dfferent commodtes are characterzed by dfferent degrees of postonalty, whch s meant to mply that the extent to whch the margnal utlty of consumpton s drven by relatve consumpton concerns dffers among goods. Solnc and Hemenway (2005) show that some commodtes are more postonal, for example the sze of one s 3

6 house s more postonal than health and safety n ther nvestgaton 1. By means of survey-expermental methods, Alpzar et al. (2005) also confrm that most ndvduals tae nto account relatve ncome and relatve consumpton of partcular goods. In addton, Solnc and Hemenway (2005) show that some publc goods le natonal defence, or space exploratons are thought to be more postonal than some prvate commodtes n a cross-natonal comparson. For example, 81% of the respondents n ther experments would be more satsfed f the natonal defence spendng n ther countres were ahead of that n other countres, whle the weght n outft for job ntervews - a prvate good- comparson s 62%. Thrdly, a part of the lterature explores the relatonshp between postonal and envronmental externaltes. Howarth (2006) characterzes the nteractve relatonshp between carbon doxde emssons taxes and a pre-exstng ncome tax n a framewor featured by the appearance of both postonal and envronmental externaltes. In ths study, the exstence of relatve consumpton concerns rases optmal emsson taxes, snce relatve consumpton effects lower the socal benefts of consumpton and ncreases socal margnal wllngness to pay for a cleaner envronment. The optmal emsson tax s characterzed by a dramatc ncrease from 63 dollar per tonne n 2005 to 384 dollar per tonne n Wthout relatve concerns, the tax would rse from 44 dollar per tonne to 229 dollar per tonne n the same tme nterval. Hs conclusons support relatvely hgh envronmental taxes when confronted wth relatve consumpton concerns. 1.3 revous studes There s an extensve lterature concernng correctve taxes to solve envronmental problems caused by the consumpton of envronmentally harmful commodtes. gou (1920) ntated a standard polcy nstrument, a gouvan tax, to nternalze negatve externaltes, whch s often cted n lterature on envronmental economcs. Sandmo (1975) dscussed optmal commodty taxaton when one of the commodtes generates a negatve externalty. In hs model, commodty taxes are the only avalable nstruments through whch the polcy maer redstrbutes and nternalzes the externalty. An 1 For health and safety ssues, days of llness, the frequency of car breadown, etc. are ncluded n the nvestgaton. espondents are less lely to compare health, for example the days of llness,than the sze of one s house. They would therefore not accept the scenaro of havng comparatvely fewer days of llness as long as they agree to ncrease the absolute days of feelng not well. 4

7 mportant result n Sandmo s study s the addtvty property, whch means that the value of the margnal externalty enters addtvely n the tax formula for the externalty generatng good, whle t has no drect effect on the polcy rules for the other commodty taxes. rttlä and Tuomola (1997) analyze the nfluence of envronmental externaltes, generated by the consumpton of a specfc good, n a mxed tax framewor, where the set of tax nstruments ncludes proportonate commodty taxes on and a non-lnear ncome tax. rttlä and Tuomala assume that earnngs-ablty s prvate nformaton not observed by the government, n whch case the optmal tax polcy must satsfy an ncentve constrant. The results show, among other thngs, that Sandmo s addtvty property carres over to a model where the polcy maer has access both to ncome and commodty taxes. Aronsson and Blomqust (2003) dscuss cross-natonal border envronmental problems n an nternatonal framewor, under nternatonal labor moblty and asymmetrc nformaton about earnngs-ablty. Ther contrbuton was to compare the optmal structure of mxed taxaton mplct n a non-cooperatve Nash-equlbrum wth the optmal tax structure mplct n a cooperatve equlbrum. Most of the revewed lterature, though, focuses on models wth only envronmental externaltes, whch omt an nteractve relatonshp between an envronmental externalty and other types of externaltes such as those emanatng from consumpton comparsons. An excepton s Howarth (1996), who analyzes optmal commodty taxes and polluton taxes when relatve consumpton effects and envronmental externaltes are caused by the consumpton of postonal commodtes. Hs study s based on a model of a sngle country. The consumer s preferences n hs model are defned over prvate consumpton of postonal commodtes, relatve consumpton compared to other domestc consumers and lesure. He furthermore sets lesure as a numerare good. The optmal commodty tax s characterzed by the margnal rate of substtuton between average consumpton level of postonal commodtes and lesure. The optmal polluton tax s featured by the margnal rate of substtuton between polluton and consumpton of postonal commodtes wth an upward adjustment factor. Ths analyss s however confned to a sngle country, so he does not consder nternatonal externaltes. 5

8 There s a growng lterature on the optmal tax polcy mplcatons of relatve consumpton concerns based on one-country models, for example Oswald (1983), orneo and Jeanne (1997), Ljungqvst and Uhlg (2000), Aronsson and Johansson-Stenman (2008) and Wendner (2010). Aronsson and Johansson-Stenman (2015) extend the analyss to a two-country model. Ther study focuses on optmal non-lnear ncome taxaton n an nternatonal framewor when postonal externaltes wor both domestcally and nternatonally. Smlar to ths nternatonal framewor analyss, Aronsson and Johansson-Stenman (2014) use a two-country model to derve areto Effcent polcy rules for the provson of natonal as well as global publc goods, where relatve consumpton matters for consumers n each country. Nevertheless, these studes do not address envronmental externaltes caused by the consumpton of postonal commodtes. In most cases the optmal commodty tax wll be underestmated, f the postonal good gves rse to envronmental externaltes, and consumers wll overvalue the consumpton of postonal commodtes n pursut of an enhanced socal status. 1.4 ontrbuton and outlne Ths paper maes two contrbutons compared to prevous studes. Frstly, we analyze postonal and envronmental externaltes n an nternatonal framewor to construct a globally optmal correctve commodty tax. We extend the analyss of Howarth (1996) to a global economy wth nternatonal externaltes, where we compare the correctve tax polcy mplct n a non-cooperatve Nash- and Stacelberg-equlbrum, respectvely, wth the correctve tax polcy mplct n a cooperatve equlbrum. Ths also means that we extend the analyss of Aronsson and Johansson-Stenman (2015) to a case where the consumpton also gves rse to envronmental externaltes. Secondly, we extend our model under nternatonal cooperaton by ncorporatng the provson of a publc good, polluton abatement. In ths broader framewor, publc good provson taes away resources from prvate consumpton when prvate consumpton can generate externaltes. ontrary to Aronsson and Johansson-Stenman (2014), the results presented below show that relatve consumpton concerns do not modfy the polcy rule for publc good provson, as long as the margnal wllngness to pay for envronmental qualty s measured n terms of the numerare, non-postonal good. 6

9 In secton two, we set up a one-country model as a benchmar to fnd an optmal commodty tax, when the consumpton causes postonal and envronmental externaltes. In secton three, we extend our benchmar to a two-country model ncludng noncooperatve behavor, such as Nash competton and Stacelberg competton, and cooperatve behavor where overall postonal and envronmental externaltes are taen nto analyss. In secton four, we ncorporate an envronmental polluton abatement varable to extend the two-country model. The socal planner uses revenues from commodty taxes and lump-sum taxes to fnance the expendture on publc abatement. Secton fve concludes that postonal and envronmental externaltes have mportant mplcatons n optmal commodty taxes and the socal wllngness to pay for polluton abatement. 2. One-country model 2.1 references and ndvdual behavor The model conssts of one country wth fxed populaton. For smplfcaton, we assume that all ndvduals are dentcal and normalze the populaton to one. The utlty functon faced by the representatve ndvdual s gven by,,,,,, U. (1) The ndvdual has preferences over two prvate goods, a non-postonal good and a postonal good. For good an ndvdual consumer both cares about hs or her absolute and relatve consumpton compared to others. Two externaltes come from the consumpton of postonal goods. One externalty comes from relatve consumpton compared wth other people, where denotes the reference consumpton level facng the ndvdual and s expressed by the average consumpton of postonal goods. The other externalty s envronment polluton f ( ), where 0 olluton here comes from each ndvdual s consumpton of postonal commodtes. Ths s nterpretable to mean that the polluton depends on the aggregate consumpton of the drty good, snce we have normalzed the populaton to equal one.. 7

10 The functon () s twce contnuously dfferentable and assumed to be ncreasng n,, and decreasng n. We can also see that decreases n, snce decreases n, whch means the hgher the average consumpton of the postonal good, the lower the consumer s utlty, ceters parbus. We set good as a numerare, therefore the prce of t s set to unty. Suppose that tax nstruments consst of a proportonate commodty tax and a lump-sum transfer T. The government poses a consumpton tax on the postonal commodty, so the relatve prce of good s q 1. The government uses the tax revenue to transfer a lump-sum payment to each ndvdual. Each consumer treats the commodty tax, ncome W, lump-sum payment T, the average consumpton of and polluton exogenously. The tme endowment for each ndvdual s normalzed to one and s completely used to wor, snce we do not ncorporate lesure n our model. Ths smplfcaton enables us to fnd an optmal commodty tax more smoothly. The budget constrant facng the consumer s then wrtten as W T q (1 ). (2) The representatve consumer s maxmzaton problem can be expressed by frst-order condtons wth respect to and, whch gves us a further mplcaton that the prvate margnal rate of substtuton between and equals to the relatve prce 1. (3) For vsual smplfcaton, we use to represent, to represent,etc., where subscrpts denote partal dervatves Degrees of postonalty We follow Aronsson and Johansson-Stenman (2015) to use degrees of postonalty. The degree of postonalty measures the margnal utlty of relatve consumpton over the total margnal utlty of consumpton. In ths secton, we defne as the degree 8

11 of postonalty. It can be explaned as the fracton of the overall utlty ncrease of an addtonal dollar spent on good that s due to ncreased relatve consumpton. We can also nterpret as the margnal externalty per unt of consumpton of good. 2.2 Optmal tax polcy We assume the government has no dffculty n allocatng socal economc resources. The optmzaton problem s to choose,,, to maxmze consumer s utlty, subject to several constrants. The government needs to allocate economc resources between and. Due to the tradeoff effect between the tax revenue and the transfer payment, where T s an endogenous varable for the government, we can combne the publc budget constrant and prvate budget constrant to derve the socal resource constrant as W. Moreover, the maxmzaton problem subjects to (4) based on the assumpton of dentcal ndvduals, where the government treats as an endogenous varable, and the polluton producton technology constrant f ( ). (5) Then the optmzaton problem becomes choosng,,, to maxmze the followng Lagrange functon,,, 1 ( ) L W f. (6) By nspectng the correspondng frst-order condtons (See Appendx A4-A10), we can see f ' 1 ( ), (7) ombnng the consumer s F.O.s (3) wth socal F.O.s (7), we can get the optmal tax on the postonal commodty (See Appendx A10-A11) f ' ( ). (8) 9

12 ostonal and envronmental externaltes caused by the consumpton of the postonal good drve a dfference between the prvate and socal benefts of consumpton changes. The frst term of represents the socal margnal wllngness to pay to avod the postonal externalty measured n unts of the non-postonal commodty. The second term represents the socal margnal wllngness to decrease polluton, adjusted by the extent the change of contrbutes to polluton producton. Because the representatve ndvdual s utlty functon ncreases n,, whch ensures 0 and decreases n,whch ensures 0, and the polluton ncreases n, whch ensures follows that 0. f ' ( ) 0, t Furthermore, the optmal tax can be wrtten as MS / f ( ), (9) ' where and MS /. The frst term n (8) can be changed nto MS /. MS/ s stll nterpreted as the socal wllngness to pay to avod the postonal externalty, but expressed as the margnal externalty per unt of consumpton of good, multplyng by the margnal rate of substtuton between the postonal and non-postonal good. In extreme cases, f 1, whch mples 0 only the relatve consumpton of the postonal commodty matters, then (9) taes the form MS / f ( ). As a hgher tax s needed to curb postonal externaltes, ' wll ncrease accordngly. For 0, whch means 0, only the absolute consumpton of the postonal commodty matters, then f ' ( ) wll hold. decreases accordngly for ths case that there exst only envronmental externaltes. If the postonal commodty has only relatve consumpton effects, then the optmal commodty 10

13 ' tax % MS s lower than MS / / f ( ), snce t s not necessary to correct envronmental externaltes. 3. Two-country model 3.1 references and ndvdual behavor The model conssts of two countres, and wth fxed populaton. For smplfcaton, we assume that the ndvduals n each country are dentcal and normalze the populaton n each country to one. The utlty functon faced by the representatve consumer n country s gven by,,,,,,,, U S. (10) The ndvdual s utlty s defned over two prvate goods a non-postonal good and a postonal good, domestc relatve consumpton, foregn relatve consumpton S and polluton. S s one dstncton compared to our benchmar model, where s the average consumpton of the postonal good n country. Besdes postonal externaltes, there are envronmental externaltes, where envronment polluton s defned by f (, ), where 0 and 0. olluton here has spllovers, whch means the polluton from country wll negatvely affect ndvdual s utlty n country, and vce versa. As n our benchmar model, s twce contnuously dfferentable and assumed to be ncreasng n,,, S and decreasng n. We can also see that decreases n and, snce and S decrease n and respectvely, whch means the hgher the average consumpton of postonal goods, the lower the consumer s utlty, ceters parbus. The government n country executes a consumpton tax on postonal commodtes and uses the tax revenue to transfer a lump-sum payment T to each ndvdual, where the representatve consumer treats, T, W, and as 11

14 exogenous. Then smlarly the representatve consumer s budget constrant can then be wrtten as W T (1 ). (11) The ndvdual s correspondng frst-order condtons regardng the two types of consumpton tradeoff can be expressed as the prvate margnal rate of substtuton between the postonal and non-postonal commodty equates to ther relatve prces (See Appendx A12-A15) S 1. (12) Agan for vsual smplfcaton, we use to represent, to represent, S to represent S country. etc., where subscrpts denote partal dervatves and superscrpts represent The degree of postonalty n an nternatonal framewor We stll follow Aronsson and Johansson-Stenman (2015) to use degrees of postonalty to measure the margnal utlty of relatve consumpton over the total margnal utlty of consumpton. The degree of postonalty has a broader meanng, snce we extend our benchmar model to a two-country model, where prvate margnal consumpton contans an addtonal term S, margnal nternatonal postonal externalty. The domestc postonalty for country s expressed by S. It s nterpretable to mean the fracton of the overall utlty ncrease of an addtonal dollar spent on good that s due to ncreased relatve consumpton for the representatve consumer n country. We can also nterpret as the margnal domestc externalty per unt of consumpton of good S. The foregn postonalty for country s gven by, where S reflects the margnal nternatonal externalty per unt of consumpton of good. 12

15 Smlarly, and S S foregn postonalty respectvely. S denote country s domestc and 3.2 Optmal tax polcy and non-cooperatve behavor In ths secton, we wll address two polcy outcomes n non-cooperatve behavor. We start wth the polcy mplcatons of Nash equlbrum where the governments n each country tae the decson made n the other country as gven n secton Then we extend to a Stacelberg equlbrum n secton 3.2.2, where the leader behaves dfferently compared to a Nash compettor by loong nto hs follower s reacton functon Nash competton The objectve of the government n country mples the maxmzaton of U, where postonal and envronmental externaltes caused by domestc consumpton of postonal commodtes are consdered, whle the two externaltes caused by foregn consumpton of postonal commodtes reman unnternalzed. The decson maer n country need to choose,,, to maxmze consumers utltes subject to several constrants. Because of the tradeoff effect between the commodty tax revenue and the payment transfer, the resource constrant for country s government can then be wrtten as W. (13) Besdes the resource constrant, the maxmzaton problem also subjects to as t s n our benchmar model, where country s government treats as an endogenous varable and constrant s as an exogenous varable, and the polluton producton technology f (, ). (14) Then the optmal tax can be derved by choosng,,, to maxmze the followng Lagrange functon,,,, 1 (, ) L W f. (15) 13

16 The frst-order condtons, defned from the perspectve of country, allow us to get (See Appendx A16-A22) S f 1. (16) ombnng the representatve consumer s F.O.s wth socal F.O.s from the pont of country, we can get the optmal commodty tax under a Nash equlbrum (See Appendx A22-A23) NE f. (17) As n our benchmar model, the frst term of NE represents country s socal margnal wllngness to avod the postonal externalty. The second term represents the socal margnal wllngness to avod polluton, adjusted by the partal effect on polluton producton made by the change of country s average consumpton. Because the representatve consumer s utlty functon ncreases n,, whch ensures 0 and decreases n,whch ensures 0, and the polluton ncreases n f whch ensures 0, t follows that 0 NE. and, The optmal tax can also be wrtten as f NE MS /, (18) where and MS / S S. The socal wllngness to avod the postonal externalty s expressed by the degree of domestc postonalty multplyng by the prvate margnal rate of substtuton between the postonal and non-postonal good. In extreme cases, f 1, whch mples 0, 0, only domestc relatve consumpton of the postonal commodty matters, then (18) taes the form S 14

17 f NE MS x/ c. As hgher taxes on postonal commodtes are needed to curb more domestc postonal externaltes, NE wll ncreases accordngly. For 0, whch means domestc relatve consumpton of the postonal commodty doesn t matter, then NE f wll hold. NE decreases accordngly to the case that there exst only envronmental externaltes. If the postonal commodty has only postonal externaltes, then the optmal commodty tax ~ NE s most lely lower than snce t s not necessary to correct envronmental externaltes. NE f, In Nash competton, the government n country can use gouvan-le tax to nternalze the postonal and envronmental externaltes affectng people wthn ts own country. Nevertheless, the externaltes affectng country are totally gnored ountry s a Stacelberg leader The possblty that there s a dfference between countres ablty to commt to publc polcy maes us tae nto account Stacelberg case where one country acts as a leader and the other s a follower. We assume country s a leader and country s a follower. Although the government n country wll behave same as a Nash compettor, the optmzaton condtons for country change, snce though the follower stll treats as an exogenous varable, the leader treats as an endogenous varable. More specfcally, the reacton functon ( ) comes from the Stacelberg competton, where country adjusts ts average consumpton of the postonal good when country changes and s therefore part of the decson problem of the leader. Thus, welfare effects on country that are caused by the altered behavor of country, whch s n turn nduced by country wll be taen to correct the arsng externaltes. 15

18 Subsequently, subject to the same constrants as n Nash competton, the optmzaton problem n country can be descrbed by choosng,,, to maxmze the followng Lagrange functon,,, ( ), 1 (, ) L W f. (19) The correspondng frst-order condtons gve us (See Appendx A24-A30) S S f f 1. (20) ombnng the consumer s F.O.s (12) wth the socal F.O.s from the pont of country when country s a Stacelberg leader (18), we can get the optmal commodty tax for the leader (See Appendx A30-A31) S f f stacelberg. (21) The dstncton between stacelberg and NE are the terms related to a reacton functon, where S and f are proportonate to. The term S represents the socal margnal wllngness to pay to avod the postonal externalty caused by country, adjusted by country s reacton functon. The term represents the socal margnal wllngness n pursut of better envronmental qualty, where f f wors as a magnfyng or decreasng factor. The socal margnal wllngness to pay for a cleaner envronment dffers from that n NE,snce t contans f,whch requres the leader to consder country s reacton effect nduced 16

19 by the change of country s consumpton. If 0,then f f exceeds f, there wll be a stronger socal wllngness n country to mprove envronment qualty, and S wll be postve, whch allows us to get stacelberg 0. We could then expect stacelberg, though the terms NE and f n stacelberg are not necessarly dentcal to those n NE under dfferent allocatons. Whle f 0, the results under the condton 0 can t be ensured. In addton, the optmal commodty tax for the Stacelberg leader can be wrtten as f f stacelberg MS / MS /. (22) The socal margnal wllngness to pay to avod the postonal externalty caused by country can be expressed by the degree of foregn postonalty, multplyng by the margnal rate of substtuton between the postonal and non-postonal good. ompared to NE, stacelberg then addtonally depends on the degree of foregn postonalty and the relatonshp between and. Nevertheless, the nternatonal postonal and envronmental externaltes are stll not nternalzed. Therefore there wll be potental welfare gans for the two countres f they can cooperate together to solve all externaltes. 3.3 Optmal tax polcy and cooperatve behavor In the case dstortons are nternatonal postonal and envronmental externaltes, a socally optmal resource allocaton can be acheved by gouvan taxaton on a global level. The cooperatve equlbrum depends on a hypothetcal socal planner, who decdes tax polces for both countres and. Suppose that there exsts a global decson-maer, who dsposes perfect nformaton and has no dffculty n economc resource allocaton 17

20 as well as tax and expendture polcy selecton across natonal borders. The global socal planner ams to realze areto optmal allocaton by maxmzng country s utlty subject to a mnmum utlty restrcton for country, an overall resource constrant and the polluton constrant. The constrants and are based on the assumpton of dentcal ndvduals n each country. The socal planner poses a proportonate tax coop on postonal commodtes n country and coop n country, and uses the tax revenue to transfer a lump-sum payment T to each consumer n country and T to each consumer n country. Thus, the consumer s budget constrant n country s gven by W T (1 ), whereas T T s the global socal planner s budget balance. The coop coop representatve consumer n country stll treats coop, T, W and coop as exogenous, whch mples that the representatve consumer s behavor s stll descrbed by (12). Due to the tradeoff effect between the commodty tax revenue and the payment transfer, the overall resource constrant can be wrtten as W W. (23) The polluton constrant s f (, ), (24) and mnmum utlty restrcton for country s U U, (25) where,,,,,,,, (, ) U S f. Then the global socal planner s optmzaton problem becomes choosng,, to maxmze the followng Lagrange functon, (, ),, m m m L U 1 W f U U. (26) m, m,, 18

21 By nspectng the correspondng socal frst-order condtons from the pont of country, we get the socal margnal rate of substtuton between the postonal and non-postonal good (See Appendx A32-A41) S S f 1. (27) The consumer s F.O.s and the socal F.O.s allow us to get the optmal tax n an nternatonal cooperatve framewor from the pont of country. Smlarly, we get country s optmal taxaton on the postonal good (See Appendx A41-A43) coop S f, (28) coop S f. (29) Snce the two countres are dentcal by assumpton, there wll be a symmetrc equlbrum, where the global socal planner chooses dentcal polces for the two countres. We therefore concentrate on the analyss of the representatve country. coop s expressed by the sum of margnal wllngness to pay, measured over both countres, to avod postonal externaltes, plus the global socal margnal wllngness to decrease the polluton generated n country, where the partal effect on polluton producton caused by the change of country s average consumpton of the postonal good wors as a multplyng factor. The dstnctons compared to the polcy mplcaton under Nash competton are descrbed by the appearance of S and f. The change of average consumpton, wll nfluence consumer s utlty both n country va domestc comparsons and that n country va nternatonal comparsons. Thus coop s featured by S. In addton, snce all envronmental externaltes are consdered, there exsts a stronger global socal wllngness to curb polluton, because an ncrease n 19

22 wll cause more total polluton, whch n turn gves country more motvatons to prevent polluton. Thus, we could expect coop NE numercally. The economc ntuton behnd ths nequalty s that the global socal planner ams to nternalze all nternatonal postonal and envronmental externaltes. A hgher correctve commodty tax s needed to prevent overconsumpton n pursut of an enhanced socal status compared wth global consumers at the cost of envronmental degradaton. onsequently, coop n country less motvatons to consume the postonal commodty. Meanwhle be wrtten as gves consumers can coop f coop MS / MS /. (30) Smlarly, coop can also be wrtten as f coop MS / MS /. (31) ompared to the optmal taxaton n Nash competton, country s foregn postonalty and margnal rate of substtuton between the postonal and non-postonal good, enter as addtonal terms. The sum of margnal socal wllngness to pay, measured over both countres, to avod postonal externaltes n s symmetrc to that n coop. The coop global socal margnal wllngness to prevent envronmental degradaton s dentcal for the two countres. The dstncton s descrbed by the dfferent partal effects on polluton producton. 4. Extenson to envronmental polluton abatement In realty, besdes a correctve tax, there are many other polcy nstruments n polluton abatement, for example drectly cleanng envronment wth government s ncome. Also, the nternatonal framewor where relatve consumpton effect s a part of consumer s utlty and global envronment s a publc good yelds dfferent polcy mplcatons of publc good provson. 20

23 We mae an extenson of the two-country model n an nternatonal cooperatve framewor by addng the provson of polluton abatement. The global socal planner uses revenue from commodty taxes and lump-sum taxes to fnance the publc expendture. From the pont of country, the representatve consumer s utlty functon s stll gven by,,,,,,,, U S. (10) The only thng that has changed s that s now defned n a dfferent way. f (, ; A ), where A s the publc expendture on abatement and 0. The A socal planner poses a proportonate tax coop on postonal commodtes n country and coop n country, and uses the tax revenue to transfer a lump-sum payment T to each consumer n country and T to each consumer n country. Ths way, the consumer s budget constrant n country s gven by W T (1 ), whereas T T A s the global socal planner s budget balance. The coop coop representatve consumer treats, coop T, W, representatve consumer s behavor s stll descrbed by (12). 4.1 ooperatve solutons of publc good provson coop and A exogenously. Then the We assume the technology of polluton abatement provson expressed by the margnal rate of transformaton between prvate and publc good s one. Due to the tradeoff effect between the commodty tax revenue and the transfer payment, the overall resource constrant s then descrbed by W W A, (32) where the global planner needs to consder how much nput s used for polluton abatement. The polluton constrant now becomes f (,, A ). (33) 21

24 Then the optmzaton problem for the global planner can be descrbed as choosng,,,,,, A to maxmze the followng Lagrange functon m m m L U 1 W A f A U U. m, m, (34) (,, ) From ths, we can get an mportant polcy mplcaton (See Appendx A44-A52), 1 f 1 1 A. (35) The shadow prce of polluton abatement nput measured n terms of the socal planner s margnal utlty of ncome s expressed by the global margnal wllngness to pay for a cleaner envronment multplyng by polluton abatement effcency, where f A wors as an adjustment factor. We arrve at the same polcy rule for publc good provson that would follow wthout any postonal concerns. The reason s that we have expressed the margnal wllngness to pay for the publc good n terms of the numerare. Aronsson and Johansson-Stenman (2014), however, expressed the margnal wllngness to pay for the publc good n terms of a postonal prvate good. onsequently, dfferent from ther results, the polcy mplcaton of publc good provson we derve remans unaltered wth the appearance of relatve consumpton concerns. 5. onclusons A consumpton tax on postonal commodtes s ndspensable to prevent overconsumpton snce postonal externaltes lead to welfare costs. In addton, some postonal goods are also lely to cause envronmental damage. The envronmental polcy decded on a natonal level cannot correct all postonal and envronmental externaltes caused by the consumpton of postonal commodtes. In order to nternalze nternatonal postonal and envronmental externaltes, each 22

25 polcy-maer must tae nto consderaton other country s margnal wllngness to pay to avod postonal and envronmental externaltes. We could expect that the optmal tax derved n a cooperatve framewor exceeds that derved n non-cooperatve framewors, whch mples a stronger wllngness for the preventon of overconsumpton and envronmental degradaton from a global socal planner s perspectve. In our model, the sum of socal margnal wllngness to pay, measured over both countres, to avod postonal externaltes s symmetrc between country and. The global socal margnal wllngness to pursue a better envronment s dentcal for the two countres. In an nternatonal cooperatve framewor, the polcy of effcent provson of polluton abatement mples relatve consumpton concerns do not modfy the polcy rule for publc good provson, where the socal margnal wllngness to pay for the publc good s measured n unts of the numerare, non-postonal good. Ths mplcaton s dfferent from Aronsson and Johansson-Stenman (2014), snce the socal margnal wllngness to pay for the publc good they expressed s measured n terms of a postonal good. Meanwhle, the optmal taxaton s based on the same prncples wth and wthout the provson of polluton abatement. We have set up our benchmar research of optmal commodty taxaton under nternatonal postonal and envronmental externaltes by characterzng the polcy nstruments n an nternatonal cooperatve framewor. There s, however, stll a lot of wor due n ths drecton of research. Questons such as the mplcatons of a framewor contanng more than two countres or multple postonal goods that could yeld dfferent results concernng the optmal taxaton and smlar questons reman unanswered. Two possble alteratons of the model appear the most promsng. Frstly, we could get a further extenson by consderng asymmetrc nformaton for example dfferent labor s earnngs-ablty, analyzed by rttlä and Tuomola (1997), Aronsson and Blomqust (2003), Ecerstorfer and Wendner (2013), Aronsson and Johansson-Stenman (2015), snce the assumpton of dentcal consumers and no cost of searchng nformaton for a polcy maer s easly challenged. Secondly, dynamc analyss may very well be our future concern. The statc model we set up s wea n explanng polluton accumulaton, because t s a dynamc process and 23

26 supported by a fact that the present volume of pollutant s determned by annual emsson and envronment tself has a lmted cleanng capablty. Thus the optmal taxaton n our statc analyss mght not ensure a areto effcent allocaton. In addton, the rcher structure of a dynamc model allows us to get closer to realty. As shown by Howarth (2006), ntertemporal aspects play an mportant role for optmal taxaton of externalty generatng goods. 24

27 Appendx The proof of equaton (3) 1 L U W (1 ) (A1) (A2) (1 ) (A3) (A2) and (A3) 1 The proof of equaton (8) f ' ( ),,, 1 ( ) L W f (A4) The correspondng frst order condtons allow us to get 1 (A5) f ' 1 ( ) (A6) (A7) (A5) and (A6) ' 1 f ( ) 1 (A8) (A6) and (A7) 1 (A9) (A8) and (A9) f ' 1 ( ) (A10) (A3) and (A10) f ' ( ) (A11) The proof of equaton (12) S 1 25

28 L U W T (1 ) (A12) (A13) (1 ) (A14) S (A13) and (A14) S 1 (A15) The proof of equaton (17) NE f,,,, 1 (, ) L W f (A16) The correspondng frst-order condtons are 1 (A17) f S 1 (A18) (A19) (A17) and (A18) 1 S f 1 (A20) (A17) and (A19) 1 (A21) S f (A20) and (A21) 1 (A22) (A15) and (A22) NE f (A23) The proof of equaton (20) S f f stacelberg,,, ( ), 1 (, ) L W f (A24) 26

29 1 (A25) 1 f f S S (A26) S S (A25) and (A26) 1 f f 1 (A27) (A28) (A25) and (A27) 1 (A29) S S (A28) and (A29) f f 1 (A30) (A15) and (A30) S f f stacelberg (A31) The proof of equaton (28) coop S f m m m L U 1 W f U U (A32) m, m, (, ) 1 (A33) f S 1 S (A34) 1 1 f S (A35) (A36) (A37) 27

30 (A33) and (A34) 1 S f 1 1 (A33) and (A37) 1 1 S (A38) (A39) (A35) 1 1 (A40) S S f (A38) (A39) and (A40) 1 (A41) (A15) and (A41) coop S f (A42) Smlarly (A35) (A36) and (A37) coop S f (A43) 1 f The proof of equaton (35) 1 1 A m m m L U 1 W A f A U U (A44) m, m, (,, ) 1 (A45) f S 1 S 0 (A46) 1 f S 1 S 0 0 f 1 0 A 1 f (A45) (A47) (A49) and (A50) 1 1 A (A47) (A48) (A49) (A50) (A51) 28

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