Trade Liberalization, Foreign Aid, and Welfare under Unemployment and Cross-border Pollution

Transcription

1 Trad Libraliation, Forign Aid, and Wlfar undr Unmploymnt and Cross-bordr Pollution Nikos Tsakiris, Panos Hatipanayotou and Michal S. Michal August 2007 (Prliminary Draft) Abstract W construct a two-country gnral quilibrium modl of forign aid, with unmploymnt in th rcipint country and cross-bordr pollution from this country to th donor. Pollution is ntirly abatd by th rcipint s privat and public sctors. W xamin th optimal rspons of th two countris in trms of th si and us of aid, and in trms of nvironmntal policis in raction to two xognous shocks. First, an improvmnt in th trms of trad as a proxy of frr trad and globaliation. Scond, a dcras in th rcipint s minimum wag as a rform proxy of its labor markt. W xamin cass whr such changs may lad to wlfar improvmnt in both countris, accounting for th optimal adjustmnts of thir policy instrumnts. Kywords: Forign Aid, Cross-bordr Pollution, Pollution Abatmnt, Unmploymnt, Minimum Wag. J.E.L Classification: F35, H41, J64, Q28 Dpartmnt of Intrnational and Europan Economic Studis, Athns Univrsity of Economics and Businss; 76, Patission str., Athns , Grc. Dpartmnt of Intrnational and Europan Economic Studis, Athns Univrsity of Economics and Businss; 76, Patission str., Athns , Grc, and CESifo (Cntr for Economic Studis and th Ifo Institut of Economic Rsarch). Dpartmnt of Economics, Univrsity of Cyprus; P.O. Box Nicosia, CY 1678, Cyprus, and Csifo. Corrspondnc: Panos Hatipanayotou, Dpartmnt of Intrnational and Europan Economic Studis, Athns Univrsity of Economics and Businss; 76, Patission str., Athns , Grc. Tl. ( ) , Fax. ( ) , mail: hatip@aub.gr 1

2 Trad Libraliation, Forign Aid, and Wlfar undr Unmploymnt and Cross-bordr Pollution 1. Introduction Throughout th past dcads country officials, intrnational organiations and policy makrs hav strongly argud that intrnational transfrs (i.., forign aid), both montary and non-montary, from dvlopd to dvloping conomis can allviat acut global and national conomic, and oftn, non-conomic problms. For xampl, it has bn maintaind, and ampl mpirical vidnc confirms, that untid or tid to spcific objctivs provision of funds is mad from dvlopd to dvloping countris for purposs of consumption, of financing capital accumulation, for provision of public goods and public inputs, of nvironmntal prsrvation, or of promoting structural rforms in commodity and factor (.g., labor) markts. 1 Such transfrs primarily aim at improving wlfar in th rcipint countris, but oftn can bnfit, ithr dirctly or indirctly, th donor countris as wll. 2 Morovr, during th long history of forign aid btwn donor and rcipint countris, thr has bn frqunt and prolongd variability both in th volum of aid offrd by th donor countris, and in th way aid has bn usd by th rcipints. On th on hand, issus such as aid fatigu, or appropriat us of forign aid by th rcipint countris, or thir complianc to th trms of rciving (tid) forign aid, hav bn among th rasons invokd by dvlopd-donor countris to incras or dcras aid to th dvloping world. On th othr hand, rcipint countris optd to us forign aid in ways most fitting thir own conomic and non-conomic objctivs rgardlss of clauss imposd on thm by th donors for th disbursmnt of th rcivd aid. Asid of th abov, howvr, changs in th global conomic nvironmnt,.g., frr intrnational trad or gratr dgr of markts globaliation, or conomic conditions in th donor or th rcipint countris, may account for changs in both th si and us of forign aid, 1 Burnsid and Dollar (2000) provid an xtnsiv rviw of conomic motivation rgarding th donation of forign aid. 2 Although th logic of aid is to bnfit th rcipint countris, quit frquntly aid has bn usd as a policy instrumnt to affct th trms of trad btwn donor and rcipint countris in favor of th formr. This issu has bn th subjct mattr of a larg litratur on th so-calld transfrs paradox (.g., s Cassn 1988, Kmp 1992). Th objctiv of th prsnt analysis, howvr, is not on this issu. 2

3 and in othr policy instrumnts. Such changs may ntail important wlfar implications for both th donor and rcipint countris. Hr, motivatd by such considrations, w xamin how, in th prsnc of conomic distortions, xognous shocks can affct wlfar and th optimal bhavior of donor and rcipint countris towards aid, and othr conomic policy instrumnts. Two distortions, capturing crtain conomic stylid facts, ar introducd in th analysis. Th first is production rlatd pollution missions that advrsly affct utility in both th mitting country (-is) and in nighboring (non-) mitting country (-is). This distortion capturs a major global considration for which nowadays forign aid is offrd. For xampl, th U.S., th Europan Union, but also indpndntly dvlopd countris such as Grmany, th UK, Swdn, and Japan ar among th primary providrs of xtnsiv forign aid to dvloping conomis (.g., Cntral and Eastrn Europan countris) for financing pollution abatmnt activitis (OECD, 2003). Th scond distortion is unmploymnt, du to th xistnc of a minimum wag, in th rcipint country. This distortion attmpts to captur an important structural fatur of dvloping conomis, and whos rform may constitut a pr-condition for aid. 3 For th purposs of our analysis two xognous shocks ar considrd. First, an improvmnt in th trms of trad as a proxy of frr trad (or globaliation) du to rducd transportation costs or du to rducd tariffs and non-tariff barrirs, and scond, a dcras in th rcipint s minimum wag as a rform proxy of its labor markt. In raction to ths shocks, w xamin (i) th optimal rspons of th two countris in trms of forign aid and nvironmntal policy, and (ii) th inducd wlfar ffcts for th two countris accounting for th optimal policy adjustmnts. 2. Litratur Rviw Various aspcts of intrnational trad and nvironmntal policy ar rlatd to th prsnt study,.g., forign aid, changs in trms of trad, minimum wag, privat and public abatmnt of cross-bordr pollution. To th bst of our knowldg ths aspcts ar not yt synthsid in a singl study. This synthsis, motivatd by th stylid facts 3 Drgulation of labor markts and th rmoval of barrirs in commodity markts (.g., tariffs and othr import barrirs) ar among th factors which dtrmin how donors allocat aid among multi-rcipint countris (.g., s, Lahiri and Raymondos-Möllr 1997, and Lahiri t al., 2002). 3

4 outlind in th introduction, constituts th primary contribution of th prsnt chaptr. For th purposs of our analysis w classify th rlvant intrnational trad litratur in two strands. Th first focuss on th links btwn forign aid and nvironmntal protction. Th scond focuss on th so-calld doubl-dividnd of nvironmntal policy rforms (i.., raising mploymnt and rducing pollution), in opn conomis with pollution xtrnalitis and unmploymnt du to xognous (i.., minimum) or noncomptitiv wag dtrmination. 4 Rgarding th first strand, a numbr of studis hav xamind th intraction among forign aid, pollution and wlfar, undr th xistnc or not of cross-bordr pollution. Rcntly, for xampl, in a modl with ndognous trms of trad and without cross-bordr pollution Chao and Yu (1999) xamin th wlfar ffcts of aid tid to public abatmnt activitis in a pollution gnrating aid-rcipint country. Hatipanayotou t al. (2002) show that vn in th absnc of intrnational coopration, cross-bordr pollution may rduc th total amount of pollution mission by inducing mor forign aid from th dvlopd to dvloping countris. Naito (2003), in a modl with ndognous trms of trad, transboundary pollution and without nvironmntal rgulation, shows that untid aid is Parto-improving in trms of wlfar if th marginal propnsity to consum in th donor country is sufficintly largr than that in th rcipint. Turunn-Rd and Woodland (2004), among othrs, xamin a varity of Partoimproving multilatral nvironmntal rforms whn compnsating intrnational lumpsum transfrs ar assumd or tariff rform is combind with th mission tax rforms. Lastly, Schwinbrgr and Woodland (2006) in a modl of tid aid, cross-bordr pollution and simultanous provision of privat and public pollution abatmnt invstigat cass whr tid forign aid may not b ffctiv in rducing pollution. Th scond strand of th litratur xamins whthr an nvironmntal tax rform provids th doubl-dividnd i.., an improvmnt of th nvironmntal quality and an allviation of th unmploymnt problm (.g., s, Bovnbrg and van dr Plog 1996 and 1998, Hol 1997, Koskla and Schöb 1999). According to this litratur 4 A siabl litratur on intrnational conomic aspcts of cross-bordr pollution is not of dirct rlvanc hr (.g., Ludma and Wooton, 1994, Copland and Taylor 1995, and Copland, 1996). Copland (1994) xamins th wlfar implications of nvironmntal and trad policy rforms in a full mploymnt small opn conomy. 4

5 nvironmntal tax rvnu is usd to cut taxs on labor or othr distortionary taxs. For xampl, Bayindir-Upmann and Raith (2003) argu that in th high tax countris a rvnu-nutral nvironmntal tax rform undr non-comptitiv labor markts yilds a positiv mploymnt ffct whil th nvironmntal dividnd is hardly attainabl. 3. Th Modl W considr a two small opn conomis gnral quilibrium modl, faturing forign aid from a donor dvlopd to a rcipint dvloping country, cross-bordr pollution and unmploymnt in th rcipint country du to th xistnc of a minimum wag. Hron, astrisks indicat all variabls of th donor country. Both countris produc, undr prfctly comptitiv conditions, two goods. For analytical simplicity of th rsults w call, good 1 th numrair xportd commodity and good 2 th nonnumrair importd on. W assum that both conomis ar small in world commodity markts so that th intrnational rlativ pric of good 2, ( p ), is xognous. 5 An analytical implication of this assumption is that both countris can xport and import th sam commoditis vis-à-vis th rst of th world. Morovr, with constant world commodity prics forign aid and cross-bordr pollution constitut th intrnational linkags btwn th two countris. Dtails rgarding this fatur of th modl ar givn latr on in th analysis. Ths goods ar frly tradd in intrnational markts, and svral primary factors ar usd in thir production. Th ndowmnts of ths factors in both countris ar fixd and factor markts ar prfctly comptitiv. Full mploymnt of all factors is nsurd in th dvlopd donor country, whil in th dvloping country involuntary unmploymnt of labor occurs du to th xistnc of a minimum wag ( w ) abov th markt-claring wag lvl. This minimum wag is assumd to b binding throughout th analysis, and thrfor, labor supply ( L) in th rcipint country is infinitly lastic and smallr than th conomy s labor ndowmnt ( L ) at th prvailing 5 Th prsnt modl can dpict, intr alia, th cas of two countris in th Europan Union, an old dvlopd mmbr-country (.g., Grmany, Franc) and a nw post-accssion, lss-dvlopd, country (.g., Slovakia, Cch Rpublic) affctd by cross-bordr pollution, with fr trad btwn thm and constant intrnational commodity prics. In this contxt, it is plausibl to assum that ths countris ar pric takrs in a much biggr world trading systm. From th viwpoint of th chaptr, this simplification (i.., constant trms of trad) facilitats th analysis whos primary objctiv is not to xamin intrnational trad issus. 5

6 wag ( w ). Pollution is gnratd in th rcipint dvloping conomy as a by-product of production and is transmittd to th dvlopd donor country in th form of cross-bordr pollution. All pollution abatmnt is undrtakn in th rcipint country by privat producrs and th public sctor, in a mattr to b xplicitly dfind soon aftr. Th donor country nithr gnrats nor dos it abat pollution. Both countris suffr disutility from local or cross-bordr pollution. W first lay out th gnral quilibrium modl of th rcipint dvloping conomy with unmploymnt and production gnratd pollution and thn th modl of th donor dvlopd country. As notd abov, pollution in th rcipint country is partly abatd by th privat sctor in rspons to an missions tax ( t) imposd by th govrnmnt, and partly by th public sctor. Th lvl of public sctor pollution abatmnt is dnotd by g importd by th country s govrnmnt at a constant world commodity pric ( p ) g, and financd through mission tax rvnu and a fraction of th rcivd aid. Following Nary (1985), in th prsnc of factor pric rigiditis, th production sid of th aid rcipint conomy can b dscribd by th rstrictd rvnu function dfind as: 6 R( pt,, υ, w) = R( pt,, υ, L) wl, (1) whr R( p, t, υ, w) max { px tr wl:( x,, L) ( υ) } = Φ, υ dnots th conomy s vctor of th flxpric factor ndowmnts. Sinc ths ndowmnts ar assumd fixd, vctor υ is omittd from th rst of th analysis. Φ (υ ) is th country s aggrgat tchnology st including both production and pollution abatmnt tchnologis by th privat sctor, 7 and x is th vctor of nt outputs. Th function R( pt,, υ, w) is th incom of th flxibl pric factors and adding to it, th incom of th fix-pric factor labor i.., wl, givs R( pt,, υ, L), th unconstraind rvnu function capturing th conomy s total valu of production (GDP), or total factor incom. From Hottling s Lmma, th partial drivativ of th unconstraind rvnu function with rspct to ( t), i.., 6 For th gnral proprtis of this function and rlatd issus s Nary (1985). Krickmir (2005) also follows th Nary approach in charactriing th supply sid of an conomy with unmploymnt du to a minimum wag. 7 For simplicity w considr only on typ of pollution gnratd in on or mor sctors. 6

7 R ( ptl,, ) dnots th lvl of pollution missions nt of privat abatmnt (s t Copland 1994). Th function R is assumd strictly convx in th mission tax rat, i.., R tt > 0, and whn accounting for changs in mploymnt partial drivativ with rspct to L R = R R R R > 0. Its tt tt tl LL Lt givs th lvl of th minimum wag, i.., R (,, ) L ptl = w. (2) Th abov condition dtrmins th lvl of mploymnt of th fix-pric factor, labor. Th function R is assumd strictly concav in L, i.., R < 0. Taking into account both privat and public sctor pollution abatmnt, th nt mission of pollution is dfind as: = R ( p, t, L) g. (3) t Th following assumptions ar maintaind throughout in ordr to facilitat th analysis: LL (A1): R tl < 0. In viw of (3) this assumption implis that an incras in th lvl of mploymnt raiss outputs and th lvl of production gnratd pollution. (A2): R tp < 0, and whn accounting for changs in mploymnt R = R R R R < 0. tp tp tl LL Lp Accounting for (A1) and (A2) it follows that th importd good, is th polluting commodity 8 and it is labor intnsiv i.., R > 0. Givn th two assumptions, an improvmnt in th trms of trad or a dcras in th minimum wag always causs a trad off btwn unmploymnt and th aggrgat lvl of pollution. On th on hand, a trms of trad improvmnt rducs pollution missions by inducing th polluting sctor to contract, and on th othr hand aggravats unmploymnt. Similarly, a dcras in th minimum wag allviats unmploymnt and incrass pollution missions. Lp R > 0 8 Othrwis if th xportd good is th polluting good thn. tp 7

8 Sinc both conomis ar considrd small in world commodity markts, both can b considrd xportrs or importrs of th sam commodity to or from th rst of th world. Clarly this assumption is not valid in th prsnc of trms of trad ffcts. Hr, w assum that both countris ar importrs of th non-numrair good and thus, an improvmnt in th trms of trad of both th donor and th rcipint countris is statd in th following assumption. (A3): dp < 0 indicats an improvmnt in th trms of trad of both th donor and rcipint countris. As for th public sctor, w assum that th govrnmnt financs th cost of publicly providd pollution abatmnt, i.., trt ( p, t, L), and by allocating a fraction λt of aid (1 λ)t pg g, through th mission tax rvnu, 9 i.., of th aid rcivd. Th rmaining fraction is assumd to b lump-sum distributd to th country s housholds. In th prsnt contxt, w do not rquir for th rcipint country to provid matching funds for th aid rcivd. That is λ 1. Thus, th govrnmnt s budgt constraint is writtn as: p g = tr ( p, t, L) + λt. (4) g t Turning to th dmand sid of th conomy, utility, as prviously notd, is advrsly affctd by locally gnratd nt pollution ( ). Th bhaviour of th houshold sctor is summarid by th xpnditur function pu (,, ) which dnots th minimum xpnditur rquird to achiv a givn lvl of utility p whn th lvl of nt pollution is with rspct to (u ), i.., u u at constant commodity prics. Th partial drivativ of th xpnditur function, dnots th rciprocal of th marginal utility of incom. Sinc pollution advrsly affcts houshold utility, th partial drivativ of th xpnditur 9 Brtt and Kn (2000) rport that in th US it is common for nvironmntal taxs to b armarkd for spcific nvironmntally rlatd public xpnditur,.g., th financing of clan-up activitis or of road construction and of public transport ntworks. Th 2000 OECD rport of th Task Forc for th implmntation of th nvironmntal action programms for th Cntral and Eastrn Europ, rports that th Kaakhstan s Law of Environmntal Protction in 1999, stipulats that... It should b prohibitd to spnd mony from Environmntal Protction Funds for purposs not connctd with nvironmntal protction.... Rvnus for ths nvironmntal funds ar listd to com primarily from pollution chargs, non-complianc fins and intrnational assistanc (aid) for nvironmntal protction. 8

9 function with rspct to, i..,, is positiv and dnots th housholds marginal willingnss to pay for a rduction in pollution (.g., s Chao and Yu, 1999). That is, a highr lvl of nt pollution rquirs a highr lvl of spnding on privat goods to mitigat its dtrimntal ffcts so that a constant lvl of utility is maintaind. Also, > ( < )0 p assuming that goods and clan nvironmnt ar substituts (complmnts) in consumption. 10 Th xpnditur function is assumd strictly convx in, i.., > 0. That is, a highr lvl of nt pollution raiss th housholds marginal willingnss to pay for its rduction. It is also assumd that th numrair good (s Lahiri and Raimondos- Möllr 1998). spnding, i.., = 0 implying that all incom ffcts prtain to u Th budgt constraind of th rprsntativ consumr rquirs that privat pu (,, ) is qual to total factors incom, i.., R( ptw,, ) + wl, plus th fraction of aid lump-sum distributd, i.., (1 λ)t constraint is writtn as:. Thus, th rcipint country s budgt ur (,, p) = R( ptw,, ) + wl+ (1 λ) T. (5) For th donor country w assum that all factors ar fully mployd. Morovr, as prviously notd, w assum that th country nithr gnrats nor dos it abat pollution. Dnoting by θ th rat of cross-bordr pollution from th rcipint country, th wlfar of th donor is advrsly affctd by th rcipint s lvl of pollution i.., = θ. Th donor s xpnditur and th rvnu functions ar thus givn by ( p,, u ) by: and R ( p ) rspctivly. Th country s incom-xpnditur idntity is givn (,, ) = ( ). (6) p u R p T Equations (2), (4), (5) and (6) constitut a systm of four quations in four unknowns, namly uu,, g and L. Th modl contains thr policy instrumnts: th amount T of aid 10 Standard proprtis of th function ar that is th (vctor) of compnsatd dmand functions, and that pp pu (,, ) is non-positiv. p 9

10 for th donor country, and for th rcipint, th missions tax rat t and th fraction λ of aid allocatd to public pollution abatmnt. Th xognous paramtrs ar th trms of trad p and th rcipint country s minimum wag rat w. Following Copland and Taylor (2003, ch. 4), an improvmnt in th trms of trad can b intrprtd as a dcras in trad costs of th icbrg typ, thus rprsnting trad libraliation Appndix A lays out th complt comparativ statics of th rducd form systm. 3.1 Pollution and Wlfar Effcts in th Donor and Rcipint Countris W conclud this sction by xamining how changs in th policy and xognous paramtrs affct th lvl of pollution and wlfar in th two countris. Changs in th lvl of pollution ar givn by diffrntiating quation (3) and using th rsults from Appndix A to obtain: d = Tp g dλ λp g dt + ( t pg) R tt + R t p g dt + ( t pg)r tlr LLp g dw + R p 1 ( t p ) dp (7) tp g g An incras ithr in th amount of aid, i.., dt > 0 or in th fraction of forign aid allocatd to public pollution abatmnt, i.., dλ > 0 unambiguously rducs th lvl of production gnratd pollution in th rcipint country. An incras in th rcipint s mission tax rat i..,t, on on hand, rducs pollution missions by th privat sctor, i.., R t. On th othr hand, this rduction in th lvl of pollution missions rducs th tax bas for th provision of public abatmnt which xacrbats th lvl of pollution. A priori, th ffct of a highr mission tax on th lvl of pollution is ambiguous. Howvr, a highr missions tax rducs th lvl of pollution if th mission tax rat (t ) is lowr than th unit cost of public abatmnt ( p g ). That is, if t p g < 0. A dcras in th rcipint s minimum wag has an ambiguous ffct on th lvl of pollution. On th on hand, th lowr w raiss production in th rcipint country and thus it raiss pollution missions. On th othr hand, highr production implis a largr tax bas, highr mission tax rvnu for financing public abatmnt and thrfor lowr lvl of pollution. A sufficint condition for th lowr w to lowr (rais) th nt pollution lvl in 10

11 th rcipint country is that t p g > 0( < 0). In th cas whr th mission tax rat quals th unit cost of public abatmnt i.., t = p g, thn a chang in minimum wag has no dirct ffct on th lvl of pollution. An xognous improvmnt in trms of trad (i.., dp < 0 ) rducs th pollution lvl in th rcipint country if th mission tax rat is lowr than th unit cost of public abatmnt i.., t p g < 0 and undr (A2). Th lvl of pollution in th rcipint country worsns if t p g < 0 and th country xports th polluting good, i.., of public abatmnt thn a chang in th trms of trad has no dirct ffct on th lvl of pollution. As prviously notd, sinc th donor country nithr gnrats nor it abats pollution, i., R tp > 0. In th cas whr th mission tax rat quals th unit cost = θ, thn, as a rsult of policy inducd or paramtr changs, changs in th lvl of cross-bordr pollution affcting th donor follow dirctly th inducd changs in. Using th rducd form systm of Appndix A w obtain th inducd changs in th lvl of countris wlfar as follows: Δ du = A dt + A dλ + A dt + A dw + A dp, and (8) T λ t w p Δ = p du BT dt Bλ dλ Btdt Bwdw B dp, (9) whr th xprssions and th sign of th cofficints in th abov quations ar givn in Appndix B. Also rcall from Appndix A that Δ ( = p R ) < 0. u u g LL From quations (8) and (9) w conclud th following. An incras in th amount of forign aid to th rcipint unambiguously incrass wlfar in that country, whil it may also incras th wlfar of th donor. Sinc in th rcipint country thr is no aid co-financing, incrasd aid raiss housholds ral incoms and public pollution abatmnt. Both ffcts xrt a positiv impact on th rcipint country s wlfar. Thus, AT in quation (8) is of ngativ sign. On th othr hand, B T in quation (9) has an ambiguous sign. In th absnc of cross-bordr pollution, i.., θ = 0, highr aid to th rcipint country unambiguously rducs th donor country s wlfar. Howvr, in th 11

12 prsnc of cross-bordr pollution, i.., θ > 0 and undr th assumption that part of th aid to th rcipint country is usd for public pollution abatmnt, incrasd aid to that country may rvrs th ngativ dirct ngativ impact on th donor s wlfar. An incras in th fraction of aid allocatd to public pollution abatmnt raiss th rcipint country s wlfar if th housholds marginal willingnss to pay for pollution abatmnt xcds th unit cost of g, that is if > p g. 11 In such a cas w say that thr is social undr-provision of public abatmnt, and A λ in quation (8) is of ngativ sign. On th othr hand, bcaus of cross-bordr pollution, an incras in λ unambiguously raiss th donor country s wlfar, i.., B λ < 0. An incras in th rcipint s mission tax rat, according to th xprssion A t of Appndix B, affcts th country s wlfar through thr channls. First, th trm Δ R p R ( = R ) u LL g t u t dnots a ngativ impact on wlfar capturing a transfr of rsourcs from th privat to th public sctor, and thus a loss in privat ral incoms. Th scon d trm Δ u t pg R [( ) tt + R t ] R LL capturs th wlfar impact of th highr mission tax through its inducd impact on th country s lvl of pollution missio ns, i.., Δ u pg( d/ dt) R LL. If, following th discussion of quation (6), th highr tax lowrs th lvl of pollution, thn through this trm it also xrts a positiv impact on wlfar. Finally, th last trm Δ p wr u g Lt, following Assumption (A1), capturs a ngativ tax inducd mploymnt-ffct on th country s wlfar. That is, assuming that th highr () t rducs th marginal rvnu product of labor (i.., R < 0), which in turn rducs mploymnt and labor incoms and it affcts Lt ngativly th rprsntativ houshold s wlfar in th rcipint country. Exprssion B t shows that th highr mission tax unambiguously improvs th donor s wlfar in that country as long as it rducs pollution missions in th rcipint, i.., du = θ 1 ( d / dt ). Clarly in th absnc of cross-bordr pollution, changs in u t do not affct th donor country s wlfar. A sufficint condition for th lowr 11 Whn > p thn thr is social undr-provision of public abatmnt ( g ). g 12

13 minimum wag to rais th rcipint country s wlfar is that t p g > In this cas, howvr, th lowr w unambiguously incrass th donor country s wlfar. If t p g < 0, thn th lowr w may rduc th rcipint s wlfar, whil it unambiguously rducs th wlfar of th donor. Th xprssion A p in Appndix B givs th wlfar impact of an improvmnt in th trms of trad (i.., dp < 0 ) in th rcipint country. Th first trms capturs th standard wlfar ffct du to a trms trad improvmnt (i.., M ). Th scond trm, du to th xistnc of unmploymnt, indicats that via th is trm, th dcras in p affcts ngativly th rcipint s wlfar by rducing of mploymnt and labor incoms in th country (i.., pwr R > 0 ). Finally, th last 1 g LL Lp trm ( t p ) R is th nvironmntal ffct of th trms of trad improvmnt on th g tp rcipint s wlfar. Following th rlvant discussion of quation (8), this trm xrts a positiv impact on th country s wlfar if t < 0, and undr (A1) and (A2). By p g obsrving xprssion B p of Appndix B, an analogous discussion can b carrid out rgard ing th impact of dp < 0 on th donor s wlfar. 4. Nash Equilibrium Having accountd for th pollution and wlfar quations, w now charactri th non-cooprativ Nash quilibrium valus of th policy instrumnts. That is w dtrmin th lvls of th policy instrumnts, (, tˆ ˆ λ) for th rcipint and ( Tˆ ) for th donor country, rspctivly, assuming that th two countris simultanously maximis thir own wlfar, trating th othr country s policy paramtrs as givn. Th symbol ( ^ ) ovr a policy variabl indicats its Nash quilibrium valu. Th first ordr conditions ar givn by: du Δ = A t = dt 0, (10) 12 Using quation (7) in quation (8) w can writ du > 0 iff ( d / dw ) > 0, which rquirs t p g > 0. du =Δ p [ w R ( d / dw)] dw. Thn u g LL 13

14 Δ du d λ = Δ du dt = A B λ T =, and (11) 0 = 0. (12) Equations (10)-(12) giv th bst-rspons functions and simultanously dtrmin th Nash quilibrium valus of th policy instrumnts in th two countris. Manipulating ths quilibrium conditions, w obtain th following Nash quilibrium conditions: = p, (13) g tˆ = p w ( R R ) R, and (14) 1 g LL tt Lt p g = λθ. (15) Rcogniing that pollution is a public bad and its abatmnt is a public good, Nash quilibrium condition (13) rprsnts th Samulson rul for th optimal provision of public goods in a closd conomy without distortionary taxation. That is, th housholds marginal willingnss to pay for public pollution abatmnt is qual to th marginal cost of producing it. Condition (14) can b viwd as a modifid, in th prsnc of unmploymnt, Pigouvian rul for th optimal provision of public goods. First, in th absnc of unmploymnt, condition (14) combind with condition (13), rducs to th xact Pigouvian rul for optimal public good provision. That is, th housholds marginal willingnss to pay for public abatmnt is qual to th mission tax rat, i.., t = = p. Howvr, as condition (14) indicats, in th prsnc of unmploymnt, this rul is no longr valid. In particular, undr (A1), i.., R < 0, in th prsnt cas w hav that th Lt g Nash quilibrium mission tax rat () tˆ is lowr that th corrsponding Pigouvian rat (i.., t = p g ) in ordr to account for its dtrimntal impact on mploymnt. Givn th xistnc of cross-bordr pollution, and th assumption that a fraction ( λ) of aid to th rcipint country is usd by th lattr country to financ th provision of public abatmnt, th condition (15) can b viwd as a modifid Samulson rul of optimal aid. 14

15 5. Exognous Shocks, Optimal Policy Rspons and Wlfar Effcts Having dscribd th Nash quilibrium of this two-country modl, as givn by \quations (10)-(12), w procd to valuat how th Nash quilibrium valus of th policy instrumnts chang du to changs in xognous variabls. That is, w xamin how dos an improvmnt in th trms of trad, a proxy for trad libraliation or conomic globaliation, 13 or a dcras in th rcipint country s minimum wag (i.., dw < 0 ), a proxy for a labor markt rform, affct th valus of tˆ, ˆ λ and ˆT. W also xamin th wlfar ffcts of ths xognous shocks accounting for th adjustmnts in th two countris Nash valus of thir policy instrumnts. In doing so w xamin thr diffrnt cass: Cas 1: On of th two countris is inactiv. That is, ithr th rcipint country adjusts th Nash valus of its policy instrumnts ( t, λ ), whil th donor dos not adjust th Nash valu of aid. Or, vic-vrsa. Cas 2: Th rcipint country adjusts only th Nash valu of ( λ) and th donor th Nash valu of ( T ). Cas 3: Th rcipint country adjusts only th Nash valu of ( t) and th donor th Nash valu of ( ). T 14 Cas 4: Th rcipint country adjusts th Nash valus of its policy instrumnts ( t, λ ) and th donor th Nash valu of ( T ). In ach of th cass abov, w assum that th initial valus of th policy instrumnts ar at thir Nash lvl. Th rducd form systms and th cofficints of th unknowns for ach of th abov cass ar givn in Appndix C Cas 1: On of th two countris rmains inactiv. 13 Copland and Taylor (2003) considr th notion of an improvmnt in th trms of trad as a notion of trad libraliation. Th sam notion is followd, in a diffrnt contxt by Hatipanayotou t al. (2005). 14 In cass 2 and 3 it is as if assuming that th rcipint country is fr to us th othr instrumnt to achiv slfish intrsts. 15 Hron, for simplicity and tractability of th rsults, w assum that all third ordr drivativs ar ro. Th authors provid upon rqust dtaild calculations of th rsults. 15

16 Considr first th cas whr th rcipint country adjusts th Nash valus of its policy instrumnts ( t, λ ), whil th donor rmains inactiv. Thn, diffrntiating (10) and (11) w obtain: Adt+ A dλ = A dw Adp, and (16) tt tλ tw tp A dt + A dλ = A dw A dp. (17) λt λλ λw λp Th ffct of a dcras in th minimum wag on th rcipint s valus of (, tˆ ˆ λ ) ar summarid in th following Corollary: Corollary 1: A dcras in th rcipint country s minimum wag raiss th country s Nash valu of th missions tax rat and it rducs th Nash valu of th fraction of aid allocatd to public pollution abatmnt. Discussion: Using quations (C.1) w obtain: dtˆ = ( RLLR d ˆ λ tt ) RLt < 0, and = ( TRLLR tt ) RLtRt > 0. (18) dw dw Th lowr minimum wag raiss labor s marginal rvnu product, and thus mploymnt. As a rsult production and production-gnratd pollution missions ris. Consquntly, th Nash valu of th mission tax rat incrass. On th othr hand, th lowr minimum wag rducs th Nash valu of th fraction of aid allocatd to financing th provision of public abatmnt. As prviously notd th lowr minimum wag by incrasing production and pollution missions it raiss th govrnmnt s mission tax rvnu usd for financing public abatmnt. Thus, th Nash fraction ˆλ of forign aid allocatd by th rcipint to financ a givn lvl of public abatmnt falls. Turning to th wlfar ffcts of th dcras in w, accounting for th adjustmnts in ˆλ and ˆt w procd as follows. Using quations (8), (9) and (18), th conditions (14) and (15), and rcalling that all trms ar valuatd at Nash quilibrium,.g., A = = 0, w obtain: t A λ 16

17 du =Δ Aw = u wr tt RLLRtt < 0, and (19) dw du d ˆ λ dtˆ Δ = Bw + Bλ + Bt = 0, (20) dw dw dw whr th right-hand-sid of quation (19) mrgs aftr substituting th optimality conditions (13)-(15) into th xprssion for B λ < 0, and that whn valuatd at Nash quilibrium both A w as givn in Appndix B. Also rcall that B w and B t ar ngativ. Intuitivly, quation (19) can b xplaind as follows. A dcras in th minimum wag rsults in highr mploymnt, outputs, and production gnratd pollution. Sinc th dcras in w unambiguously raiss th rcipint country s wlfar, th inducd positiv mploymnt-output ffct dominats th ngativ ffct du to highr pollution missions. Equation (20) indicats that th lowr w dos not affct th wlfar of th donor country. 16 Th dcras in w incurs a ngativ dirct impact on th donor s wlfar du to highr cross-bordr pollution from th rcipint country. Also, sinc th lowr w ntails a dcras in ˆλ, thus a dcras in public pollution abatmnt, mor cross-bordr pollution rsults in an additional, indirct, ngativ ffct on th donor s wlfar (i.., Δ B ( dλ / dw) > 0). Lastly, th inducd incras in ˆt (i.., dtˆ / dw < 0) ˆ λ implis mor privat pollution abatmnt, thus lss cross-bordr pollution, which xrts a positiv impact on th donor country s wlfar (i.., Δ B ( dt / dw) < 0). Th rsult in ˆ t quation (20) indicats that ths ffcts outwigh ach othr, rsulting to a ro nt ffct of th lowr w on u. Not that, qualitativly, th sam rsult, i.., ( du / dw) = 0, mrgs whn thr is no cross-bordr pollution btwn th two countris. Th ffct of an improvmnt in th trms of trad affcts on Nash valus (, tˆ ˆ λ ) ar summarid in th following Corollary: Corollary 2: Undr (A1) and (A2), an improvmnt in th trms of trad lowrs th Nash valu of th fraction of aid allocatd to public pollution abatmnt if 16 Straightforward calculations using th optimality conditions (13)-(15) and th rlvant xprssions in Appndix B lad to th rsult in quation (20). 17

18 clan nvironmnt and good 2 ar substituts in consumption. Th trms of trad improvmnt lavs unaffctd th Nash valu of th rcipint s missions tax rat () t ˆ. Discussion: Using quations (C.1) w obtain: d ˆ λ = ( T ) ( ) 1 p w pg RLLR tt RLt R tp, and dp dtˆ 0 dp =. (21) Th improvmnt in th trms of trad lads th polluting sctor of th conomy to contract in th rcipint country according to (A2). Th trms of trad improvmnt also rducs th dmand for clan nvironmnt if th lattr and good 2 ar substituts in consumption, i.., > 0. This ffct xrts a ngativ impact on th Nash valu ˆ λ of th p fraction of aid allocatd to public pollution abatmnt, i.., ( T ) R tp p > 0. Morovr, sinc by (A1) and (A2) R Lt < 0 and < 0, rspctivly, thn th scond right-hand-sid trm of ( d ˆ λ / dp) is also positiv. Thrfor, in th prsnt cas, sufficint, but not ncssary, condition for an improvmnt in th trms of trad to rduc th Nash valu of ˆ λ is that good 2 and clan nvironmnt ar substituts in consumption. If any of ths assumptions dos not hold, thn th improvmnt in th trms of trad may rais th Nash valu of ˆ λ. A chang in th trms of trad dos not affct th Nash valu of th rcipint s mission tax rat. 17 An improvmnt in th trms of trad rducs th pollution missions and thus it tnds to rduc th Nash valu of ˆt, whras a dcras in th amount of forign aid that is allocatd to public abatmnt tnds to incras ˆt in a compltly offstting way to th initial incras. Evaluating at th Nash quilibrium th wlfar implications of th trms of trad improvmnt, aftr accounting for th inducd policy adjustmnts, w obtain: 17 Using quations (C.1) and quation (6) aftr som algbra w can writ Ω ˆ 1( dt / dp) = Aλλ Atp + At λ Aλ p = Aλλ Aλ pt pg( / t) Aλλ Aλ pt pg( / t), whr p t = wr R R. g ( / ) ( LL Lt t ) 18

19 du du Δ = Ap = u ( M wrlprll + wrltrllr tt Rtt R tp ), and (22) dp dp du d ˆ λ dt ˆ Δ = + + du = + dp dp dp dp Bp Bλ Bt u ( M θ p ), (23) Undr th Assumptions of th modl quation (22) indicats that th improvmnt in th trms of trad improvs th rcipint country s wlfar if th bnficial impact on wlfar du to lowr pollution missions (i.., th trm wr R R R R < 0 capturs th Lt LL tt tt tp pollution ffct of a dcras in p ), dominats th ngativ mploymnt ffct (i.., R R w> 0 ). 18 In th prsnt contxt of unmploymnt du to a minimum wag, th Lp 1 LL standard bnficial impact (i.., incras in ral incoms) of th improvmnt in th trms 1 of trad on th country s wlfar, i.., M, is waknd du to th xistnc of unmploymnt and is nhancd du to lowr pollution missions. For th donor country, th standard bnficial trms of trad improvmnt ffct, i.., M u u, is augmntd by th additional trm u θ p. Th lattr trm also xrts a positiv impact on th donor s wlfar, du to th improvmnt in th trms of trad, if in th rcipint country th non-numrair good and clan nvironmnt ar complmnts in consumption, i.., p < 0. Now, considr th cas whr it is th donor that adjusts its Nash valu of aid, du to an incras in th rcipint country s minimum wag or du to an improvmnt in th trms of trad, whil th rcipint country rmains inactiv. Th ffcts of a rduction in w and of an improvmnt in th trms of trad on th Nash si of forign aid ar summarid in th following Corollary: Corollary 3: A rduction in th minimum wag unambiguously raiss th Nash si of forign aid. A sufficint, but not ncssary, condition for an improvmnt 18 Th xprssion for A p in quation (22) is obtaind aftr substituting in it (s Appndix B) th optimality conditions (13)-(15). 19

20 in th trms of trad to rduc (may incras) ( Tˆ ) good 2 ar substituts (complmnts) in th donor s consumption. is that clan nvironmnt and Discussion: Diffrntiating th quilibrium condition (12) i.., quations (s Appndix C) w obtain: dtˆ dtˆ = BTT BTw < 0, and dw dp TT Tp B T = 0 and using = B B. (24) Th dcras in minimum wag incrass mploymnt, production and pollution missions in th rcipint country. Givn th Nash valus (, tˆ ˆ λ ), th amount of cross bordr pollution riss, thus inducing th donor to rais th Nash si of forign aid to th rcipint. On th othr hand, an improvmnt in donor s trms of trad incrass ral incoms and dcrass th lvls of cross-bordr pollution. Sinc by (A1) and (A2) rspctivly, R < 0and R < 0, rspctivly, th trms of trad improvmnt inducs th Lt tp donor to rduc th Nash amount of forign aid whn th polluting good and clan nvironmnt ar substituts in consumption (i.., > 0 ). In th absnc of cross-bordr p pollution, ithr xognous shock, i.., dw > 0 or dp < 0, dos not affct th donor s Nash amount of aid. Th wlfar implications of th lowr w, whn th donor country adjusts its Nash quilibrium valu of aid, aftr som algbraic manipulations, ar givn as follows: du dtˆ du Δ = Aw + AT = w( urllr tt) ( Rtt λ RtLR LLRLt) < 0, and (25) dw dw dw du Δ = B ( ) w = θ u pg t RtL >0, (26) dw whr, valuatd at Nash quilibrium A = p wr R > and A w u g tt tt 0 = p R <. Th T u g LL 0 intuition of th rsult in quation (25) follows prvious discussion (.g., s quation (19)) whr by th positiv mploymnt-output ffct of th lowr w dominats th ngativ ffct du to lowr pollution missions, and thus ovrall th lowr minimum wag xrts a positiv impact on th rcipint country s wlfar. Equation (26) indicats 20

21 that, in th prsnc of cross-bordr pollution, th lowr w unambiguously worsns th donor s wlfar. Els, whn θ = 0, thn, also du / dw = 0. Turning to xamin at Nash quilibrium th wlfar implications of th improvmnt in th trms of trad, accounting for th adjustmnts in th two countris Nash valus of policy instrumnts, w obtain: du dp dtˆ A A A A B B dp Δ = p + T = p T TT Tp, and (27) du 1 Δ = Bp = pr u g LL[ M + λ ( t pg) R t p ], (28) dp Equation (27) indicats that, in gnral, th wlfar ffct of an improvmnt in th trms of trad is ambiguous. Th improvmnt in th trms of trad incrass th rcipint country s wlfar if it lads to a ris of th amount of aid rcivd i.., dtˆ 0 dp <, and also, if th bnficial impact from lowr pollution missions outwighs th ngativ impact on wlfar du to aggravation of unmploymnt. Equation (28) shows that undr th assumptions of th modl, an improvmnt in th donor s trms of trad unambiguously improvs its wlfar. Th first right hand trm capturs th standard positiv dirct ffct of an improvmnt in a country s trms of trad. Th scond trm nhancs th prvious positiv impact of th trms of trad du to lowr lvl of cross bordr pollution. Th wlfar implications of dw > 0 and dp < 0 accounting for th inducd adjustmnts in th countris Nash policy ar summarid in th following proposition. Proposition 1: Considr th cas of two small opn conomis with cross-bordr pollution, forign aid, and public pollution abatmnt and unmploymnt in th rcipint country. a. Lt, du to xognous shocks, only th rcipint country adjust th Nash valus of its policy instrumnts, whil th donor dos not, thn: (i) a dcras in th rcipint country s minimum wag raiss its wlfar, and lavs th wlfar of th donor unchangd, 21

22 (ii) an improvmnt in th trms of trad improvs th rcipint s wlfar if th pollution ffct dominats th mploymnt ffct. It improvs th donor s wlfar if good 2 and clan nvironmnt ar complmnts in consumption (sufficint condition) in th rcipint country. b. Lt only th donor country adjust th Nash amount of aid, whil th rcipint dos not adjust th Nash valus of its policy instrumnts, thn: (i) a dcras in th rcipint s minimum wag improvs th country s wlfar and it worsns th wlfar of th donor, (ii) an improvmnt in th trms of trad improvs, undr th assumptions of th modl, th donor s wlfar, and it may worsn th wlfar of th rcipint if good 2 is a substitut to clan nvironmnt in consumption in th donor country Cas 2: Th rcipint country adjusts only th Nash valu of ( λ) and th donor th Nash valu of ( T ). In this cas, diffrntiating (11) and (12) w obtain: A dλ + A dt = A dw A dp, and (29) λλ λt λw λ p BTλ dλ + BTTdT = BTwdw BTpdp, (30) Th ffcts of a rduction in th minimum wag on ( ˆ λ, Tˆ ) ar givn in th following: Corollary 4: A rduction in w unambiguously raiss th Nash si of forign aid, whil it lavs unaffctd its fraction allocatd by th rcipint to public pollution abatmnt. Discussion: Using quations (C.2), th ffct of a dcras in th minimum wag on th Nash valus ( ˆ λ, Tˆ ) ar as follows: 22

23 dtˆ 2 2 = ( λr R ) LL tt RtL w< 0, and dw d ˆ λ = dw Th dcras in minimum wag incrass cross-bordr pollution and thus inducs th donor to rais th Nash si of forign aid. An incras in th amount of forign aid tnds to rduc th fraction of aid allocatd to public abatmnt, whil an incras in th pollution missions du to xpansion of th polluting sctor in th rcipint country incrass ˆλ. Equation (31) suggsts that ths two ffcts cancl ach othr out. Thus, providd that th rcipint country maintains a constant Nash missions tax rat, i.., ˆ 0 dt = (31), whil th donor raiss its Nash quilibrium amount of aid, th rcipint country, at th Nash quilibrium, dos not chang th fraction pollution abatmnt. ( ˆ λ) of aid allocatd to public Th ffct of th lowr w on th two countris wlfar, accounting for th inducd adjustmnts in th Nash quilibrium valus of aid and fraction of aid, ar givn as follows: du dtˆ du Δ = Aw + AT = ( urllr 2 tt) w[ Rtt ( λrll) RtL] < 0, and (32) dw dw dw du du 2 Δ = θ u ( pg t) RtL > 0 = wθ ( u pg ) RLt R tt RtLRLL > 0. (33) dw dw Th positiv ffct of th lowr minimum wag on th rcipint country s wlfar follows th intuition of th rsults in quations (19) and (25). Equation (33) indicats an unambiguous worsning in th donor s wlfar du to th rduction in th rcipint country s minimum wag. An improvmnt in th trms of trad ntails th following ffcts on th Nash valus of λ andt : d ˆ λ = λ( ) ( θ p p ), and (34) dp 19 Using quations (C.1) and (C.2) aftr som algbraic manipulations w can writ d ˆ λ / dw= ( λr R ) wr A B + ( λr R ) wr A B = 0. LL tt tl λt TT LL tt tl λt TT 23

24 dtˆ dp 1 = ( λ ) λt( p θ p ) + ( p + ( t pg) R tp ). (35) Equations (34) and (35) indicat, by us of th optimality condition (15), that in th absnc of cross-bordr pollution, changs in th trms of trad do not affct th Nash valus of th two policy instrumnts. In th prsnc of cross-bordr pollution, howvr, quation (34) indicats that th sign of th ffct of an improvmnt in th trms of trad on th Nash valu of λ dpnds on th rlationship btwn good 2 and clan nvironmnt in th two countris consumption. For xampl, th sufficint and ncssary condition for th improvmnt in th trms of trad to rais ˆλ, i.., d ˆ λ / dp< 0, is that p p > θ assuming that th two ar substituts in consumption, i.., p > 0 and p> 0, and it is p < whn good 2 and clan nvironmnt ar p θ complmnts in consumption. To bttr illustrat ths rsults, th following Lmma considrs a spcial cas of th gnral analysis. Lmma 1: Suppos th two countris hav idntical prfrncs. Thn, a trms of trad improvmnt raiss (lowrs) th Nash valu of λ if good 2 and clan nvironmnt ar substituts (complmnts) in consumption (ncssary and sufficint condition). It rducs (may incras) th Nash si of T if good 2 and clan nvironmnt ar substituts (complmnts) in consumption (sufficint condition). Discussion: Making us of th assumption of idntical prfrncs, Nash quilibrium conditions (13) and (15) bcom = = p, and ths into quations (34) and (35), rspctivly, w obtain: g λθ = 1 rspctivly. Substituting d ˆ λ = dp (1 θ ) λp 1, and (36) 24

25 dtˆ dp = T(1 θ ) p + λ ( p + ( t pg ) R tp ). (37) Thn, Lmma 1 follows straightforwardly. Turning to xamin at Nash quilibrium th wlfar implications of th improvmnt in th trms of trad, accounting for th adjustmnts in th two countris Nash valus of policy instrumnts, and also assuming idntical prfrncs in th two countris, w obtain: Δ du dtˆ Ap AT dp = + dp, du u = M RLLRLpw+ (1 λ λ)( t pg) R tp + T p(1 θ ) + pλ dp (38) du dλ Δ = Bp + Bλ dp dp ˆ du 1 1 u = ( M + λ ( t pg) R tp) (1 p θ ) T. (39) dp Equation (38) indicats that, in gnral, th trms of trad improvmnt on th rcipint s wlfar is ambiguous. Th trms of trad improvmnt incrass wlfar du to th highr volum of imports, and du to th rduction in pollution missions, whil xacrbats unmploymnt problm according to th assumptions of th problm. Th last trm is th impact of th improvd trms of trad on th rcipint s wlfar through th inducd adjustmnts in th Nash amount of forign aid. Through this trm, th improvmnt in th trms of trad xrts a ngativ impact to th rcipint country s wlfar if good 2 and clan nvironmnt ar substituts in consumption. Furthrmor, th improvd trms of trad incras th donor s wlfar if good 2 and clan nvironmnt ar substituts in consumption. Finally, in th absnc of cross-bordr pollution, adjustmnts in th Nash valus of th policy instrumnts λ and T, du to th trms of trad improvmnt, do not affct ithr country s wlfar. Th wlfar implications of dw > 0 and dp < 0 accounting for th inducd adjustmnts in th countris Nash policy ar summarid in th following proposition. 25

26 Proposition 2: Considr th cas of two small opn conomis with cross-bordr pollution, forign aid, and public pollution abatmnt and unmploymnt in th rcipint country. Lt, du to xognous shocks, th rcipint country adjust th Nash valu of th fraction of aid allocatd to public pollution abatmnt, and th donor country adjust th Nash amount of forign aid. Thn: (i) a dcras in th rcipint country s minimum wag incrass its wlfar, and dcrass th wlfar of th donor country, (ii) assuming idntical prfrncs in th two countris, an improvmnt in th trms of trad incrass th donor s wlfar and may rduc th rcipint s wlfar if good 2 and clan nvironmnt ar substituts in consumption (sufficint condition) Cas 3: Th rcipint country adjusts only th Nash valu of () t and th donor th Nash valu of ( T ). In this cas, diffrntiating (10) and (12) w obtain: Adt+ A dλ = A dw Adp, and (40) tt tλ tw tp BTt dt + BTTdT = BTwdw BTp dp. (41) Th following Corollary stats th impact of a rduction in th minimum wag on th Nash valus (, tt ˆ ˆ ). Corollary 5: A rduction in w unambiguously raiss th Nash rat of th rcipint s mission tax and it rducs th Nash si of forign aid. Discussion: Using quations (C.3), th ffct of a dcras in th minimum wag on th Nash valus (, tt ˆ ˆ) ar as follows: 26

27 dtˆ = ( RLLR tt ) RLt < 0, and dw dtˆ = ( λrllr tt ) RLt Rt > 0. (42) dw A rduction in th minimum wag raiss mploymnt, outputs and production gnratd pollution. As a rsult th rcipint country s govrnmnt incrass th Nash valu () tˆ of th mission tax rat. On th othr hand, this incras in () tˆ raiss th rcipint s mission tax rvnu that is usd to financ th provision of public pollution abatmnt. As a rsult, pollution missions and cross-bordr pollution fall rsulting to a rduction in th Nash quilibrium amount of forign aid by th donor. Turning to th wlfar ffcts of th lowr w, accounting for th adjustmnts in th Nash valus of th policy instrumnts w obtain: du dtˆ du Δ = Aw + AT = ( urllr tt) ( wrtt λ RLtRt), and (43) dw dw dw du dtˆ du Δ = Bw + Bt = ( u RLLR tt) RLtRtλ < 0. (44) dw dw dw Th lowr minimum wag ntails an ambiguous ffct, through changs in th lvl of pollution missions, on th rcipint country s lvl of wlfar. On th on hand, as shown by quations (42), th inducd incras in () tˆ rsults in lowr lvls of pollution and this xrts a positiv impact on th country s wlfar. This ffct is capturd by th trm ( R R ) wr of quation (43). At th sam tim, howvr, th lowr w ntails a u LL tt tt xpansionary ffct on mploymnt and output, and thus on pollution missions which affcts th country s wlfar ngativly. This is th ( λ R R ) R R u LL tt Lt t trm of quation (43). Dpnding on th rlativ si of ths two ffcts, th lowr w may dcras or incras th rcipint s wlfar. Obsrving quation (44) w infr that th lowr w ntails a ngativ impact on th donor s wlfar du to th inducd incras in pollution as a rsult of highr mploymnt and production in th rcipint country, i.., Δ > 0, B w and a positiv on du to th inducd dcras in pollution as a rsult of th incras in th rcipint s Nash mission tax rat, i.., Δ B ( dt / dw) < 0. Givn that ˆ t 27

28 ( du / ) dw < 0th lattr ffct outwighs th formr. Thus, in this cas, th rcipint s lowr minimum wag has a bnficial ffct on th donor country s wlfar. An improvmnt in th trms of trad ntails th following ffcts on th Nash valus of λ andt : dtˆ 1 = ( θ p 1 ( g R tt ) ( wrllrlt Rt ) θ p p ), and (45) dp dtˆ dp ( θ ) = ( λθ R ) [ p ( wr R R ) 2 tt g LL Lt t p p + R w R R R R. (46) 1 ( θ tt p ( LL tt ) )] Lt tp Equation (45) indicats that th sign of th ffct of an improvmnt in th trms of trad on th Nash valu of λ dpnds on th rlationship btwn good 2 and clan nvironmnt in th two countris consumption. Following th discussion of quation (34), th sufficint and ncssary condition for th improvmnt in th trms of trad to p p rais ˆt, i.., dtˆ / dp < 0, is that > θ assuming that th two ar substituts in consumption, i.., > 0and >, and it is p p 0 p < whn good 2 and clan p θ nvironmnt ar complmnts in consumption. Equation (46) indicats that in gnral th ffct of th trms of trad improvmnt on th Nash amount of forign aid is ambiguous. Undr th assumptions of th modl, sufficint, but not ncssary, conditions for ˆT to incras as a rsult of th trms of trad improvmnt ar: (i) good 2 and clan nvironmnt to b complmnts in consumption, (ii) numrair good is th country s polluting commodity, i.., p >, and (iii) th p θ discussion of quations (34), (35) and of Lmma 1, Lmma 2 blow stats th rsults of quations (45) and (46) again for th spcial cas whr prfrncs in th two countris ar idntical. R tp > 0. Following th 28