Economic analysis of e-waste market under imperfect information

Transcription

1 Economic analysis of -wast markt undr imprfct information Prudnc Dato To cit this vrsion: Prudnc Dato. Economic analysis of -wast markt undr imprfct information <halshs-07248v2> HAL Id: halshs Submittd on 6 Aug 205 HAL is a multi-disciplinary opn accss archiv for th dposit and dissmination of scintific rsarch documnts, whthr thy ar publishd or not. Th documnts may com from taching and rsarch institutions in Franc or abroad, or from public or privat rsarch cntrs. L archiv ouvrt pluridisciplinair HAL, st dstiné au dépôt t à la diffusion d documnts scintifiqus d nivau rchrch, publiés ou non, émanant ds établissmnts d nsignmnt t d rchrch français ou étrangrs, ds laboratoirs publics ou privés.

2 Economic analysis of -wast markt undr imprfct information ϯ Prudnc Dato - August, 205- Abstract Dspit intrnational rgulations that prohibit th trans-boundary movmnt of lctronic and lctric wast (-wast), non-rusabl -wast is oftn illgally mixd with rusabl -wast and rsults in bing snt to dvloping countris. As dvloping countris ar not wll prpard to proprly manag -wast, this illgal trad has important ngativ xtrnalitis, and crats nvironmntal injustic. Th two main information problms on th -wast markt ar imprfct monitoring and imprfct information on th so-calld dgr of purity of th -wast. In this papr, w us a simpl bilatral orth-south trad modl and show that thr xists an altrnativ -wast markt that is bttr than th standard -wast markt for dvloping countris. This altrnativ -wast markt is a joint trad in rusabl and non-rusabl -wast. In both cass, w considr dmand and supply sids, plus th quilibrium of th -wast markt to show that th altrnativ markt that w propos is bttr for dvloping countris. EL classification: Q53, L5, D82, F8. Ky words: E-wast, markt, imprfct information, intrnational trad. Ϯ Corrsponding Author. (prudnc.dato@univ-savoi.fr), Univrsity Savoi Mont Blanc/ IREGE (Franc). I am gratful to my formr advisor Prof Philipp Bontms for guiding m and to th two mmbrs of jury for my dfns, Prof Stfan Ambc and Prof Cathrin Bobtchff for thir hlpful commnts. I also thank Prof Aud Pommrt for hr valuabl commnts. All rmaining rrors ar min.

3 Economic analysis of -wast markt undr imprfct information - uly, 205- Abstract Dspit intrnational rgulations that prohibit th trans-boundary movmnt of lctronic and lctric wast (-wast), non-rusabl -wast is oftn illgally mixd with rusabl -wast and rsults in bing snt to dvloping countris. As dvloping countris ar not wll prpard to proprly manag -wast, this illgal trad has important ngativ xtrnalitis, and crats nvironmntal injustic. Th two main information problms on th -wast markt ar imprfct monitoring and imprfct information on th so-calld dgr of purity of th -wast. In this papr, w us a simpl bilatral orth-south trad modl and show that thr xists an altrnativ -wast markt that is bttr than th standard -wast markt for dvloping countris. This altrnativ -wast markt is a joint trad in rusabl and non-rusabl -wast. In both cass, w considr dmand and supply sids, plus th quilibrium of th -wast markt to show that th altrnativ markt that w propos is bttr for dvloping countris. EL classification: Q53, L5, D82, F8. Ky words: E-wast, markt, imprfct information, intrnational trad.

4 . Introduction Around th world, 48.9 million tons of lctronic wast (-wast ) was gnratd in 202, which corrsponds to 9.6 kg pr capita (StEP-U, 203). Th growth of -wast is stimatd to rach 3-5 a yar, a rat that is narly thr tims that of convntional wast (UEP, 2005). A comparativ advantag in trms of labour, disparitis in nvironmntal rgulations togthr with an imprfct monitoring systm favour th -wast trad btwn rich and poor countris. As dvloping countris ar not wll prpard to proprly manag - wast, th illgal trad of -wast has important ngativ xtrnalitis and can b sn as nvironmntal injustic. In this papr, w show that th altrnativ -wast markt of joint trad in both non-rusabl and rusabl -wast is bttr for dvloping countris. Stringnt nvironmntal rgulations in dvlopd countris, togthr with a low purchasing powr of consumrs in dvloping countris, crat incntivs for th -wast trad. Within th contxt of th incrasing growth of -wast throughout th world and facing high disposal costs in dvlopd countris, 2 firms in rich countris can dcid to invst in grn dsign by incrasing th lvl of rusability of thir product (Brnard, 205). Th firms in rich countris can also sll to industris that rus -wast (Higashida, 202). As th monitoring systm is imprfct, th lattr option is oftn chosn. In fact, th -wast markt is rgulatd by a rang of intrnational rgulations such as th Basl Convntion, WEEE Dirctivs, 3 th Bamako Convntion, tc. If firms rally ar complying with intrnational rgulations, thr will b no possibility that firms from rich countris could xport th nonrusabl parts of -wast to lss dvlopd countris. Unfortunatly, this is not th cas bcaus -wast is oftn shippd back to thir countris of origin by th customs officrs of importing countris du to illgally tradd products (Higashida, 202). For instanc, in Hong Kong btwn 2006 and 2008, 29 importd shipmnts of controlld lctronic wast wr rturnd to thir countris of origin (Kojima t al., 20). Illgal shipmnt occurs not only bcaus intrnational rgulations ar wak, but also bcaus it is difficult to idntify nonrusabl -wast. 4 Hnc, th two main information problms that ar rlatd to th -wast markt ar imprfct monitoring and imprfct information on th so-calld dgr of Thr is no standard dfinition of - wast. Th trm - wast is gnrally usd for all typs of lctrical and 2 In th 980 s, th avrag disposal costs for on ton of hazardous wast in Africa was btwn US$2.50- $50, and in industrializd countris $00- $2,000 (Kummr, 995). 3 Wast Elctrical and Elctronic Equipmnt (WEEE) Dirctivs ar th lgislativ framwork within th Europan Union (EU) (EC rgulation 03/2006). 4 For instanc, it is vry costly and tim- consuming to chck a full containr of scond hand tlvisions to nsur that thy all constitut rusabl - wast. 2

5 purity. Ths two problms crat incntivs for non-valuabl -wast to b snt to poor countris. Th ngativ xtrnalitis du to th hazardous componnts of -wast ar srious bcaus dvloping countris do not hav th appropriat knowldg and/or tools to proprly manag -wast. Additionally, th mix of rusabl with non-rusabl -wast can b sn as an indirct subsidy. In fact, th xporting firm indirctly pays for th disposal srvic by lowring th pric at which it slls th -wast in dvloping countris. For xampl, th avrag pric for all tlvision sts xportd drops from 339 to 28 whn thy ar xportd to igria, Ghana or Egypt (Brnard, 205). In this contxt, w ask th following qustions: first, what ar th factors that could xplain th incras in non-rusabl -wast in dvloping countris; and scond, dos thr xist any bttr altrnativ than monitoring th standard -wast markt to rduc th trad of non-rusabl -wast? E-wast issus ar lss studid in conomics than in nvironmntal nginring and chmistry. To our knowldg, Sn (962) is th arlist contributor to th litratur on th intrnational trad in usd goods. H analyzs th potntial gains from th intrnational trad in usd goods that is basd on th movmnt of usd machinry from high to low labour cost countris. In th sam vin, Smith (976) and Bond (983) modl th gains that may crat th comparativ advantag btwn countris. This advantag may com from disparitis in nvironmntal rgulations, labour cost or wast disposal tchnologis. For instanc, trad in wast can b sn as trad in wast disposal srvics (Copland, 99). In this contxt, Copland (99) shows that it is optimally bttr to allow fr trad in wast products. H suggsts that this fr trad must b combind with intrnal tax policis and rgulations to control for th xtrnalitis, which ar rlatd to disposal. Howvr, h points out that this policy may suffr from complianc or nforcmnt issus, and thrfor may rsult in an incras of incntivs for firms to vad taxs and rgulations, and to dispos of thir wast illgally. Clrids (2008) shows th sam rsults basd on asymmtric quality standards that rduc trad in nw goods and gnrat ngativ impacts on domstic industry. Th pollution havn hypothsis (PHH) prdicts that firms will rlocat to jurisdictions with lss stringnt nvironmntal rgulations. A larg body of vidnc supporting th xistnc of PHH has bn dmonstratd by Baggs (2009), Kllnbrg (200), Brnard (205), and Kinnaman & Yokoo (20). An xcption is Higashida t al. (2008) who us a gravity modl, and show that th mor dvlopd a country, th mor it imports 3

6 rcyclabl wast. Kllnbrg (200) focuss on th consumption sid of pollution instad of th production sid of xtrnalitis to mphasiz th wast havns hypothsis. For ohnston (998), markt and policy failurs may xplain th advrs conomic and nvironmntal ffcts of an introduction of a ban on trad in hazardous wast. Latr on, Lipman (20) shows that intrnational rgulations rlating to th trans-boundary movmnt of hazardous wast undr th Basl Convntion ar not abl to protct dvloping countris. On of th main rcommndations in th Europan Topic Cntr s rport on Sustainabl Consumption and Production (ETC/SCP) trans-boundary shipmnts of wast in th Europan Union is to study th choics and bhaviour of wast producrs/collctors. otably, such a study could hlp to bttr undrstand th drivrs of this trad in ordr to rduc thir impact, and/or to adapt lgislation. To our knowldg, only Brnard (205) focuss on th stratgis of -wast producrs to xplor th driving forcs for illgal wast trad. Th analysis of th bhaviour of collctors will b an important issu in this papr. In this papr, w us a simpl bilatral orth-south trad modl, and show that thr xists an altrnativ bttr than th standard -wast markt for dvloping countris. This modl is clos to that of Brnard (205), and considrs on rprsntativ firm in th orth and on rprsntativ firm in th South. Our contribution is four-fold. First, it sms mor ralistic to analyz collctors' bhaviours than producrs' bhaviours, as it is through collctors that producrs participat in th -wast markt. Collctors can collct -wast mainly from housholds, companis or in th scond-hand goods markt. Scond, w considr that at th momnt th collctors ar collcting th -wast, thy do not know which part of th wast constituts rusabl -wast. Howvr, aftr collcting th -wast, th collctor can dcid to invst in sorting, and to sparat th rusabl wast from th nonrusabl wast. Third, bfor xporting, th collctor has incntivs to mix additional nonrusabl -wast that is illgally providd by companis in charg of disposing -wast in thir country of origin, which ar willing to pay for th disposal cost in th orth. In th cas whr th collctor dos not invst in sorting, h participats in th standard markt. Th nonrusabl -wast can probably b dtctd as illgal by intrnational monitoring systms and rturnd to th country of origin. Th collctor in this cas has to pay a fin, and can participat in th altrnativ markt that w propos by invsting in th sorting procss. Th altrnativ -wast markt is a joint trad in rusabl and non-rusabl -wast without a monitoring systm. 4

7 Th fourth is our main finding. W show that, first, firms in th orth ar willing to pay to gt rid of thir non-rusabl -wast, whil firms in th South ar willing to gt compnsation for disposal srvics. This crats incntivs for a trad in disposal srvics. Scond, in th altrnativ markt without a monitoring systm, th quantity of non-valuabl -wast is lowr than that in th standard markt at a highr pric of rusabl -wast. Thus, it can b a bttr option for firms in th South to adopt th altrnativ -wast markt, which would rsult in mor rusabl -wast and lss non-rusabl -wast, with compnsation for disposal srvics. Third, w also show that if th standard -wast markt has to prsist, only a vry high marginal pnalty will constrain firms in th orth from mixing both typs of -wast. Anothr important issu is th implmntation of this altrnativ markt. Firms in dvloping countris nd to induc firms in th orth to invst in sorting, and to truthfully rval th dgr of purity. This implmntation issu rquirs incntivs thory togthr with information larning mchanisms that can b applid to th Principal-Agnt framwork. This issu is xplord in Dato (204). Th rmaindr of th papr is organizd as follows. Th modl is dscribd in Sction 2. In Sction 3, w analyz th cas of no invstmnt in sorting, whil Sction 4 is dvotd to th cas of invstmnt in sorting with participation in th altrnativ -wast markt. W compar both cass in Sction 5. Th comparativ statics ar prsntd in Sction 6. Finally, Sction 7 concluds. 2. Th modl W propos th following framwork to dscrib th -wast markt (Fig ). W us a simpl bilatral orth-south trad modl and considr on rprsntativ firm in th orth and on rprsntativ firm in th South. This modl is clos to that of Brnard (205), who uss grn dsign stratgis to xplain th incras in th illgal shipmnt of -wast. Sh considrs that th firm in th orth producs th nw good and manags it at th nd-of-lif. Th firm in this cas can try to incras th lvl of rusability of th nw good by incorporating th disposal cost of th -wast at th nd-of-lif, or can dcid to illgally ship th -wast. In fact, most of th firms from dvlopd countris that ar involvd in -wast markts ar collctors. Th xportrs ar not th firms that produc th nw goods, hnc on may considr that thir stratgis might b diffrnt. Also, whil trading, firms in th South do not know th xact dgr of purity that is dfind as th part of rusabl scond-hand products in th import. 5

8 Figur : Concptual Framwork orth Housholds, companis, scond- hand markts, tc. Q o Sorting Invstmnt (0) D Collctor Additional non- rusabl - wast D Sorting Invstmnt C(Q) Standard - wast markt Altrnativ - wast markt X with q South Importd mix of - wast qx Importd rusabl - wast qx P Consumrs (- q)x Importd non- rusabl - wast (- q)x d s Disposal 6

9 This dgr of purity dtrmins thir dcision to trad and th quantity of -wast that thy ar willing to trad. In th orth, th lvl of illgal -wast thy ar willing to mix with th rusabl -wast dpnds on th monitoring systm, which is hadd by national authoritis through th inspction of xport (or import) matrials. It is thn important to account for th issu of imprfct information to analyz th -wast markt. Th xportr in th orth is, in gnral, a collctor. H collcts a quantity Q of -wast in th hom country through many mans. H can collct -wast from th company that has to rnw thir matrials, from housholds, from th scond-hand goods markt in his hom country, tc. In ordr to collct and xport -wast, it costs C (α,q) for th firm in th orth. Th cost function is incrasing in th quantity of -wast Q that is collctd, and th marginal cost is high whn th part of rusabl α is high. Th cost function is convx in th lvl of xport, and th marginal cost is incrasing in th dgr of purity α. Aftr collcting -wast, th firm can dcid to invst in sorting and to sparat th rusabl part αq from th nonrusabl part (-α)q. This invstmnt costs C(Q). If th collctor dcids not to invst in sorting, h will not b abl to know th dgr of purity α. Bfor xporting, th firm has incntivs to mix additional non-rusabl -wast D, that is illgally providd by companis in charg of disposing -wast in thir hom country. Ths companis ar willing to pay for th disposal cost in th orth d. In th cas whr th collctor dos not invst in sorting, h supplis th quantity of -wast X in th standard markt. Th quantity X is th sum of th quantity of collctd -wast Q and th additional non-rusabl -wast D. Thn, both typs of -wast ar mixd and sold to th firm in th South at th pric P. Th non-rusabl part in th xport is (-q) [(-α)q + D]/X, with q th dgr of purity of xport. 5 Th non-rusabl -wast (-q)x has probability σ to b dtctd as illgal by th intrnational monitoring systm and rturnd to th hom country. Th firm in this cas has to pay a fin F(q,X) which is incrasing in th non-rusabl part. On th contrary, w propos an altrnativ -wast markt that w dfin as a joint trad in rusabl and non-rusabl -wast without a monitoring systm. This altrnativ -wast markt holds if and only if th collctor dcids to invst in sorting. If h dos so, h is abl to sparat th two typs of -wast and supply to th altrnativ -wast markt. Th rusabl part αq is sold at a pric P, and th non-rusabl part (-α)q +D is sold at a pric P 0 and h bars a sorting cost C(Q). 5 ot that th dgr of purity of th xport is diffrnt from that of th collctd - wast bcaus of th additional - wast D. 7

10 Th firm in th South undr imprfct information pays P to th firm in th orth for both typs of scond-hand goods. It costs Cs(q,X) for th firm in th South to import and transform vn partially th scond-hand goods. Th cost function is incrasing in th quantity of import and th marginal cost is low whn th rusabl part is high. Th cost function is convx in th lvl of import and th marginal cost is dcrasing in th dgr of purity. Th firm in th orth gains P for rslling th rusabl part in th South and bars d s as th disposal cost that is rlatd to th non-rusabl part. Howvr, th quantity of th nonrusabl -wast that nds up in th South dpnds on th intrnational monitoring systm. In fact, at th momnt th firm in th orth dcids to mix illgal and lgal scond-hand goods, th firm in th orth dos not know for crtain whthr th xport will b inspctd or not. In th cas of th altrnativ -wast markt, th firm will pay P and P 0 for rusabl and nonrusabl -wast rspctivly. Bnfits and costs of th bilatral orth-south trad modl ar summarizd in Tabl. W us this framwork to analyz th standard and th altrnativ markts of -wast. First, w focus on th standard -wast markt that corrsponds to th imprfct information on th dgr of purity from th importr sid. In this cas, th firm in th orth dos not invst in sorting and supplis a mixd typ of -wast. Scond, w analyz th cas of prfct information on th dgr of purity and on th monitoring systm. This corrsponds to th altrnativ -wast markt that w propos. Th collctor in th orth invsts in sorting, and supplis in a joint markt of rusabl and non-rusabl -wast, whil th firm in th South dmands th sam joint markt of rusabl and non-rusabl -wast. W assum a joint trad of both typs of -wast to highlight th possibility of lgally trading non-rusabl -wast, instad of illgally mixing it. Du to th comparativ advantag in trms of labour, it may b optimal to trat -wast in dvloping countris. A transfr of appropriat tchnologis that could hlp dvloping countris to proprly dispos of -wast could follow this joint markt. Profit/ α ( σ) [( α) ] (SI) Firms in orth (Supply) Firms in South (Dmand) Bnfit Cost Bnfit Cost P Q+ P Q+ D + dd C ( α, Q) + σf( Q, D) PqX [ ( σ )( )] q q P X C ( q, X) + d ( σ )( q) X S + + S Profit/ P Q+ P0 ( ) Q+ D + dd C ( α, Q) + C( Q) α [ α ] (SI) PX PX + PX CS( X) + dsx0 Tabl: Bnfits and costs of th bilatral orth-south modl. 8

11 3. o sorting invstmnt W focus on th standard markt that corrsponds to th cas of no invstmnt in sorting. W study th markt quilibrium that is givn by dmand and supply of -wast. Π SI and ΠSI S dnot th profit without invstmnt in sorting for th collctor in th orth and that of th firm in th South, rspctivly. Both supply and dmand ar obtaind by maximizing th two profits. W assum that firms and collctors ar pric takrs in this modl, in that thy do not influnc prics. In fact, many firms in th South ar intrstd in -wast as scond-hand goods. In this way, svral collctors in dvlopd countris also hav an incntiv to gt rid of thir -wast in ordr to avoid facing costly -wast disposal. 3.. Supply (Collctor in th orth) Th Collctor in th orth solvs th following programm: (S.) maxπ SI P αq + P ( σ )[( α)q + D] C (α,q)+ d D σ F(Q, D) Q, D (S.) stats that th collctor optimally chooss th quantity of -wast that h collcts and th additional non-rusabl -wast that is mixd in ordr to gt a maximum bnfit nt of xpctd costs. Th first and scond ordr conditions with rspct to Q and D ar givn rspctivly by: (S.2) (S.3) Π SI [ ] C (α,q) Q P α + ( σ )( α) Π SI Q D F(Q, D) P ( σ ) σ D + d 0 F(Q, D) σ 0 Q (S.4) 2 Π SI Q 2 2 C (α,q) Q 2 σ 2 F(Q, D) Q 2 0 SI 2 2 Π F( Q, D) (S.5) σ D D (S.2) and (S.3) ar arbitrag conditions. Th collctor is indiffrnt btwn th xpctd additional gain from slling on additional unit of th collctd -wast or that of th additional non-rusabl -wast, and th xpctd additional costs. (S.4) and (S.5) ar scond 9

12 ordr conditions that nsur that th profit is maximal at th optimum lvls of th collctd -wast and of th additional non-rusabl -wast. Du to th proprtis of C and of F(Q,D), (S.4) and (S.5) nsur that th profit function is concav in Q and D. Thn, th first ordr conditions (FOC) with rspct to Q and D lad to an optimum lvl of th collctd -wast Q*(P ), and th optimal lvl of additional non-rusabl -wast D*(P ). Hnc th supply can b dducd as: S S(P ) Q* (P ) + D*(P ) Dmand sid (Firm in th South) Th programm that solvs th firm in th South is th following: (D.) maxπ SI S (q, X) PqX P qx ( σ )( q)p X C S (q, X) d S ( σ )( q)x X As th firm in th South could not idntify Q and D, it facs th whol packag of -wast. (S.) stats that th firm in th South optimally chooss th quantity of th mixd -wast that provids a maximum xpctd bnfit nt of xpctd costs. Th first and scond ordr conditions with rspct to X ar givn rspctivly by: (D.2) (D.3) Π SI S X Pq d S ( σ )( q) P q + ( σ )( q) 2 Π SI S X 2 2 C S (q, X) X 2 0 [ ] C S (q, X) 0 X (D.2) is also an arbitrag condition, and (D.3) nsurs that th profit is maximal at th optimal lvl of X. Thn, w can dduc th dmand function as D X(P ) Markt quilibrium By qualizing dmand and supply (D S ), w gt th quilibrium lvl of trad X*. Using X*, w can calculat D* X* - Q* and (-q) [(-α)q* + D*]/X*. From (S.2)-(D.2) and (S.3)-(D.2), w gt th following quilibrium conditions: (E.) CS( q, X) q+ ( σ )( q) C( α, Q) F( Q, D) Pq ( q)( σ) ds * + σ X α + ( σ)( α) Q Q 0

13 and (E.2) Pq ( q)( σ )d S C S (q, X ) X q + ( σ )( q) σ # F(Q, D) & * d +σ (. $ D ' Both quilibrium conditions (E.) and (E.2) stat that th rsal pric in th South of on unit of th -wast trad should b qual to th marginal costs (costs in th orth and in th South, pnalty from inspction) rlatd to th trad, and th disposal costs that ar adjustd by th probability of inspction and th dgr of purity. Th quilibrium conditions incorporat all of th paramtrs that ar rlatd to both sids of th -wast trad and to th inspction. Th ffct of ach paramtr on th quilibrium pric is not obvious. W prform comparativ statistics in Sction 6 on th abov quilibrium conditions to dduc thir ffcts. 4. Sorting invstmnt Th sorting invstmnt allows th collctor to participat in th joint trad of th non-rusabl and rusabl -wast markts. As bfor, w study th markt quilibrium, and both supply and dmand ar obtaind by maximizing th profit of ach firm. Π SI and ΠSI S ar dfind as th profit with invstmnt in sorting by th collctor in th orth and th firm in th South, rspctivly. 4.. Supply (Collctor in th orth) Th programm to b solvd by th firm in th orth is th following: (S.6) maxπ SI P αq + P 0 [ ( α)q + D ] C (α,q) C(Q)+ d D Q, D By dnoting X αq and X 0 (-α)q+d, th quantity of th rusabl -wast and that of th non-rusabl -wast rspctivly is: maxπ SI P X + P 0 X 0 C (α,q) C(Q)+ d D X 0, X Subjct to X αq and X 0 ( α)q + D Implicitly, th collctor chooss th quantity of rusabl -wast and that of non-rusabl - wast that provids maximal profit on th joint -wast markt. Th first ordr conditions ar givn by:

14 (S.7) Π SI X P C (α,q) * Q Q C(Q) X Q * Q X + d * D X 0 (S.8) Π SI X 0 P 0 C (α,q) * Q Q C(Q) X 0 Q * Q X 0 + d * D X 0 0 Q D With ; 0; Q D and. X α X X 0 α X 0 (S.7) and (S.8) bcom rspctivly: C ( α, Q) CQ ( ) (S.9) P * + * Q α Q α C ( α, Q) CQ ( ) (S.0) P0 + d * + * 0 Q α Q α (S.9) and (S.0) ar arbitrag conditions with rspct to th quantity of th rusabl -wast and to th non-rusabl -wast rspctivly. With Q*, w dduc S S (P ) and S 0 S 0 (P 0 ), bing th supply in th rusabl -wast and in th non-rusabl -wast, rspctivly. W claim on th supply sid th following: Proposition : In th cas of sorting invstmnt, th pric of non-rusabl -wast should b ngativ ; th firm in th orth should pay to gt rid of its non-rusabl -wast. Proof of Proposition : (S.9) is th wll-known rsult of prfct comptition. Th pric of th rusabl -wast is qual to its marginal cost. W can asily dduc th implicit supply function of th rusabl -wast as S S (P ). This is indd a supply function bcaus: P! 2 C (α,q) X " + 2 C(Q)! ". α 2 Q 2 Q 2 ot that th pric of rusabl -wast that is paid by firms in th South P is highr than th on in th orth. If this condition dos not hold, thn firms in th orth will prfr to sll in th hom country and thn th rusabl -wast markt will brak down. In gnral, th pric of th rusabl -wast is low in th orth du to th fact that consumrs in th orth hav lss intrst in obsolt quipmnt. 2

15 (S.0) stats that th marginal pric of th non-rusabl -wast should b qual to th marginal cost, nt of th paymnt rcivd from additional non-rusabl -wast (d ). Likwis, w can dduc th implicit supply function of th non-rusabl -wast as S 0 S 0 (P 0 ) and X 0 α *! 2 C (α,q) " + 2 C(Q) Q 2 Q 2! ". First, w assum that it is chapr to gt non-rusabl -wast than rusabl -wast bcaus th formr has lss conomic valu. It mans that th Right Hand Sid (RHS) of quation (S.0) is vry small. As nvironmntal rgulations ar stringnt in th orth, d is assumd to b high. Thn, to hav th quality in quation (S.0), th Lft Hand Sid (LHS) must also b small, and hnc P 0 must b ngativ. In this cas, firms in th orth ar willing to pay firms in th South in ordr to dispos of th non-rusabl -wast. ot that thir willingnss to pay must not xcd th disposal cost thy hav to pay in thir hom country. Othrwis, it is bttr to dispos of it locally, and this will brak down th non-rusabl -wast markt that is a part of th altrnativ -wast markt. Likwis, this is not th gnral cas Dmand sid (Firm in th South) (D.4) maxπ SI S PX P X P 0 X 0 C S (X ) d S X 0 X 0, X Th first ordr conditions with rspct to X 0 and X ar givn rspctivly by: (D.5) (D.6) Π SI!# 0 if P S P X 0 d 0 0 S " 0 $# 0 othrwis Π SI S P P C (X ) S 0 X X W claim on th dmand sid, th following: Proposition 2: In th cas of sorting invstmnt, th pric of th non-rusabl -wast should b ngativ ; th firm in th South is willing to gt compnsation for disposal srvics. Proof of Proposition 2: From (D.6) w gt that: 3

16 (D.7) P C S (, X ) X + P This rsult is a prfct comptition condition stating that th pric must b qual to th marginal cost. Th marginal cost has two componnts: th pric of on unit of rusabl - wast that is paid to th firm in th orth and th marginal cost rlatd to th rpairing fforts. For a givn pric P in th South, w can dduc a dmand function for th rusabl -wast as D D (P ). W can chck that D is indd a dmand function. Th drivativ of (D.4) with rspct to X is givn by P X C (, X ) 2 S < 2 X 0. Th dmand of rusabl -wast xists as long as th rsal pric P of th rusabl -wast in th South is highr than th pric P that is paid to th firm in th orth.!# 0 if P (D.5) lads to P 0 d 0 0 S " $# 0 othrwis. In ordr to hav an optimum dmand of th non-rusabl -wast (X 0 ), th condition (D.5) should b qual to zro. This mans that th pric of th non-rusabl -wast P 0 should b ngativ. Hnc, th ncssary condition for firms in th South to trad in th prsnc of non-rusabl -wast is to b compnsatd. W can also dduc an implicit dmand function D 0 D 0 (P 0 ). Th compnsating pric P 0 should at last b qual to th disposal cost in th South in ordr for firms thr to trad Markt quilibrium By qualizing dmand and supply (D 0 S 0 and D S ), w gt in quilibrium th lvls of trad X 0 * and X *. From (S.9)-(D.6) and (S.0)-(D.5), w gt th following quilibrium conditions: (E.3) P α *! # C(Q) + C (α,q) " Q Q! #+ C (, X ) S " X and (E.4) d d S α *! # C(Q) + C (α,q) " Q Q! #. " 4

17 (E.3) stats that th rsal pric of th rusabl -wast in th South should b qual to its marginal cost. Th marginal cost is rlatd to both firms in th orth and in th South and to th sorting invstmnt. From (E.4), w can dduc that at th quilibrium, th diffrnc in nvironmntal rgulations (disposal cost) positivly dpnds on th sum of th marginal sorting cost and th marginal cost of collcting in th orth. Th marginal sorting cost and th marginal cost of collcting in th orth ar assumd to b positiv so that th disposal cost in th orth is always highr than that in th South. 5. o sorting invstmnt vs sorting invstmnt In this sction, w compar rsults btwn th standard -wast markt and th altrnativ - wast markt at th lvls of supply and dmand. 5.. Supply sid In th supply sid, w claim th following: Proposition 3: Imprfct information on th dgr of purity without monitoring lads to a pric of -wast that lis btwn P 0 and P. Corollary : Imprfct information on th dgr of purity without monitoring lads to lss supply of th rusabl -wast and mor supply of th non-rusabl -wast. Proposition 4: In th cas of imprfct information on th dgr of purity with prfct monitoring, only high marginal pnaltis can mak th standard -wast markt lss attractiv. Proof of Proposition 3: Using (S.2) and (S.3), w can driv th implicit supply function S X(P ). It can b shown that S X(P ) is indd a supply function using th following condition: P X P Q + P D with X Q+D σ σ * 2 F(Q,D)! + * 2 C (α,q) # D 2 "!α + ( σ )( α )! " "# Q 2 +σ 2 F(Q,D) Q 2 $. & & 5

18 In ordr to compar P, P and P 0, w will considr two cass (σ0 in th cas of no monitoring, and σ in th cas of full monitoring). By assumption, th pric that holds in th standard markt is positiv for th markt to xist. Proposition shows that th pric of th non-rusabl -wast should b ngativ. This allows us to only compar th pric in th standard markt to th pric of rusabl -wast in th altrnativ markt. * o monitoring (σ0) Using (S.2) and rplacing σ0, w gt th following quations: P C (α,q) Q and P C (α,q) * Q α + C(Q) Q * α. As α is lowr than on, w can conclud that without th monitoring systm, th pric of th rusabl -wast in th altrnativ markt is highr than th pric in th standard markt, bcaus firms in th South will anticipat this and mix both typs of -wast. Proof of Corollary By using th proprtis of supply function, w can asily dduc that without monitoring, th supply in th rusabl -wast in th standard markt is lss than that of th altrnativ markt. In fact, th pric of th rusabl -wast in th altrnativ markt is mor attractiv for th firm in th orth. In th sam way, th pric of th non-rusabl -wast is lss attractiv in th altrnativ markt and inducs lss supply of th non-rusabl -wast. Proof of Proposition 4: Th full monitoring corrsponds to th cas of σ. * Full monitoring σ Likwis, rplacing σ into (S.2) lads to: P α * C (α,q) Q W can dduc th diffrnc: P P F *( α Q - C(Q) Q ). + α * F Q and P C (α,q) Q * α + C(Q) Q * α. 6

19 Dpnding on th diffrnc btwn th marginal pnalty and th marginal sorting cost, th pric of th rusabl -wast in th altrnativ markt can b highr or lss than th pric of -wast in th standard markt. If th marginal pnalty is high, thn firms in th orth will hav incntivs to invst in sorting and to avoid mixing both typs. As th altrnativ -wast markt will b full of supplirs, th consqunc is that th pric of rusabl -wast in th altrnativ markt lowrs. Thrfor, th pric of -wast in th standard markt incrass bcaus of th full monitoring and th high pnalty. Howvr, it maks th standard markt lss attractiv. On contrary, if th marginal pnalty is low, th collctors will not invst in sorting and will mix both typs which will lowr th pric of - wast in th standard markt and mak it mor attractiv. W conclud that vn with a prfct monitoring systm, only a high marginal pnalty can induc firms in th orth to avoid mixing both typs of -wast Dmand sid W claim th following: Proposition 5: Undr imprfct information, th pric of -wast in th standard -wast markt lis btwn P 0 and P. Corollary 2: Undr imprfct information on th dgr of purity, dmand for th nonrusabl -wast is lss and dmand for th rusabl -wast is high in th standard -wast markt. Proof of Proposition 5: As bfor, w can compar th pric of -wast in th standard markt to th pric of rusabl -wast in th altrnativ markt. By using (D.2) and (D.6), w hav: (P + d S )( σ )( q) +σ ( q) C S P P X!q " + ( σ )( q) # $ 0 with q ; σ W conclud that whatvr th condition is of th monitoring systm, th firm in th South has a high willingnss to pay for rusabl -wast in th altrnativ markt than -wast in th standard markt. As th pric of th non-rusabl -wast is ngativ (Proposition 2), w dduc that th pric of -wast in th standard -wast markt lis btwn P 0 and P. 7

20 Proof of Corollary 2 As th firm in th South has a high willingnss to pay for th rusabl -wast in th altrnativ markt than -wast in th standard markt, it will prfr mor rusabl - wast. Hnc, dmand in th non-rusabl -wast must b lss, and dmand in rusabl -wast must b high. 6. Comparativ statics on markt quilibrium conditions In this sction, w idntify th ffct of disposal costs, th diffrnc in nvironmntal rgulations, th rsal pric of -wast in th South, and th ffct of th monitoring systm on th quilibrium quantity and pric in th altrnativ and standard -wast markts. Proposition 6: W claim th following: Tabl 2: Comparativ statics 6 dx dx 0 dx dp dp 0 dp dp dds d(d -d S ) /- +/- dσ 0 0 +/ S th proof of Proposition 6 in Appndix I. In th altrnativ -wast markt and according to Proposition 6, th lvl of trad in valuabl -wast (rusabl) dpnds only on th rsal pric in th South. In fact, th main purpos of importing -wast in dvloping countris is for r-us. Thn, as long as th rsal pric is high in th South, th lvl of trad in rusabl -wast will incras at a high pric. Disposal costs in th orth and thos in th South do not hav any impact on ithr th pric 6 dy is th diffrntial of Y. 8

21 or th lvl of trad in rusabl -wast. Th fact that disposal costs ssntially targt nonrusabl -wast may xplain this. In fact, it is quit th rvrs, as disposal costs hav ffcts (positiv or ngativ) on non-rusabl -wast. A stringnt nvironmntal rgulation in th South will rsult in lss trad in non-rusabl -wast, whil a stringnt nvironmntal policy in th orth lads to mor trad in th non-rusabl -wast. This fact can xplain th xistnc of Pollution Havns Hypothsis. Firms in th orth may dcid to scap th high disposal costs from thir hom country and ship th non-rusabl -wast to th South at a lowr disposal cost. Howvr, in th cas whr th South incrass th disposal cost, shipping is no longr profitabl for firms in th orth. Thrfor, th lvl of trad in th nonrusabl -wast rducs. Additionally, th diffrnc btwn nvironmntal rgulation in th orth and th South has a positiv ffct on th trad of non-rusabl -wast. As long as th disposal cost is lowr in South, it will b attractiv for firms in th orth to ship th nonrusabl -wast. Howvr, th diffrnc in rgulation has an undtrmind qualitativ ffct (positiv or ngativ) on th pric of th non-rusabl -wast. Unsurprisingly, th diffrnc affcts nithr th lvl of trad in th rusabl -wast nor its pric. In th standard markt, paramtrs hav joint ffcts 7 on th lvl of trad rlativ to th altrnativ -wast markt. Th monitoring has a positiv impact on th pric of th - wast, and an undtrmind ffct on th lvl of trad in -wast. This is surprising, bcaus th monitoring is targtd to rduc th trad in -wast. But, as th lvl of trad has two componnts (rusabl and non-rusabl -wast), a high pric will induc lss non-rusabl and mor rusabl -wast. Hnc, th lvl of trad will dcras or incras, dpnding on th diffrnc btwn th dcrasing rat in non-rusabl -wast and th incrasing rat in rusabl -wast. 7. Conclusion In this papr, w us a simpl bilatral orth-south trad modl and show that thr xists an altrnativ bttr than th standard -wast markt for dvloping countris. W propos an conomic analysis of a standard -wast markt that w compar with an altrnativ markt of a joint trad in rusabl and non-rusabl -wast. W thn show that firms in th orth ar willing to pay to gt rid of thir non-rusabl -wast whil firms in th South ar willing to gt compnsation for disposal srvics. Morovr, in th altrnativ markt without a monitoring systm, th quantity of non-valuabl -wast is lowr than that of th standard 7 It is a combination of ffcts on both non- rusabl and rusabl - wast. 9

22 markt at a highr pric of rusabl -wast. Thn, it can b a bttr option for firms in th South to adopt th altrnativ -wast markt, which rsults in mor rusabl -wast and lss non-rusabl -wast with compnsation for disposal srvics. W also show that only a vry high marginal pnalty can constrain firms in th orth from mixing both typs of -wast. Thus, it should b bttr to allow a lgal -wast trad togthr with an nforcmnt of an appropriat tchnology transfr for sustainabl -wast rcycling tchnologis in dvloping countris, such as for pyromtallurgical mthods and d-gassing CFC/HCFC. Anothr important issu is th implmntation of this altrnativ markt. Firms in dvloping countris nd to induc firms in th orth to invst in sorting and to truthfully rval th dgr of purity. This implmntation issu rquirs incntivs thory togthr with information gathring thory applid to th Principal-Agnt framwork, which is xplord in Dato (204). For th sak of simplicity, w nglct in this modl factors such as th xistnc of nw products in th South, importing firms for th purpos of rcycling, markt powr to firms in th orth, production procss in orth, tc. Howvr, our modl is still valid. In fact, in th South, th majority of nw products do not last, and vn if th pric is low, consumrs may doubt th quality and prfr scond-hand products. Th xistnc of nw products may not altr th main rsults in this papr. Th modl is also still valid in th cas whr th - wast is importd for th purpos of rcycling, but thn th bhaviour of firms in th South may chang. This modl nds to b mpirically tstd, and can b xtndd to mpirically stimat th lasticity of -wast dmand and supply by using ral data from th -wast markt. It could also hlp to idntify th quantitativ ffcts of taxs through th pric, th monitoring systm, and disposal costs on th dmand, supply and th trad in -wast. Exprimntal mthods can also b usful to undrstand th stratgic bhaviour of collctors in th orth and of firms in th South. 8. Slctd Rfrncs. Baggs,., (2009) Intrnational trad in hazardous wast. Rviw of Intrnational Economics 7, Brnard, S., (205) orth south trad in rusabl goods: Grn dsign mts illgal shipmnts of wast. ournal of Environmntal Economics and Managmnt 69: Bond, E. W. (983) Trad in usd quipmnt with htrognous firms. Th ournal of Political Economy 9, Clrids, S. (2008) Gains from trad in usd goods: Evidnc from automobils. ournal of Intrnational Economics 76,

23 5. Copland, B. R., (99) Intrnational trad in wast products in th prsnc of illgal disposal. ournal of Environmntal Economics and Managmnt 20, Dato, P. (204) Inducing sorting invstmnt and implmntation of an altrnativ -wast markt undr imprfct information. FAERE Working Papr, Grubl, H. G. (980) Intrnational trad in usd cars and problms of conomic dvlopmnt World Dvlopmnt, 8(0), Harford,. D., (978) Firm bhavior undr imprfctly nforcabl pollution standards and taxs. ournal of Environmntal Economics and Managmnt 5, Higashida K. (202) Trad in Scondhand Goods, Monitoring of Illgal Trad, and Import Quotas on Lgal Trad. Discussion Papr Sris 90, School of Economics, Kwansi Gakuin Univrsity. 0. Higashida, K. and Managi, S., (2008) Th dtrminants of trad in rcyclabl wasts, th structur of rcycling sctor and th ffcts of trad rstrictions, mimo.. ohnston,. (998). Th implications of th Basl Convntion for dvloping countris: th cas of trad in non-frrous mtal-baring wast. Rsourcs, consrvation and rcycling, 23(), Kllnbrg, D. (200) Consumr wast, backhauling, and pollution havns. ournal of Applid Economics 3, Kinnaman, T., and H. Yokoo (20) Th nvironmntal consquncs of global rus. Amrican Economic Rviw 0, Kojima M., A. Yoshida, Sasaki S., and C. Sungwoo (20) Trans-boundary Movmnt of Hazardous Wast: Lssons from uncovrd cass. Kojima and Michida d., Economic Intgration and Rcycling in Asia: An Intrim Rport, Chosaknkyu Hokokusho, Institut of Dvloping Economis. 5. Krugr. (998) Prior Informd Consnt and th Basl Convntion: Th Hazards of What Isn't Known Th ournal of Environmnt Dvlopmnt 7; Kummr K. (995) Intrnational Managmnt of Hazardous Wasts. Clarndon Prss Oxford. 7. Kummr, K. (999). Intrnational Managmnt of Hazardous Wasts: Th Basl Convntion and Rlatd Lgal Ruls. Oxford Univrsity Prss on Dmand. 8. Lpawsky,. and Mcnabb, C. (2009) Mapping intrnational flows of lctronic wast. Th Canadian Gographr. 9. Lipman Z. (20) Trad in Hazardous Wast: Environmntal ustic Vrsus Economic Growth Working paprs, Environmntal ustic and Lgal Procss, Macquari Univrsity, Australia. 20. Marbury H. R. (995) Global Environmntal Racism ournal of Transnational Law, Sn, A. K. (962) On th usfulnss of usd machins. Rviw of conomic.and statistics 44 : Smith, M. A. M. (976) Intrnational thory in Vintag Modls rviw of conomic studis 43: StEP-U (203), E-wast world map, onlin country lvl data. 24. UEP (2005) E-wast, th hiddn sid of IT quipmnt s manufacturing and us rport, Environmntal Alrt Bulltin. 2

24 9. Appndix I Proof of proposition 6: Th proof is dividd into thr cass. Th first two cass ar rlatd to th altrnativ -wast markt whil th last cas concrns th standard -wast markt. Cas : Th rusabl -wast in th altrnativ -wast markt. W us th supply X S (P ) and th dmand X D (P,P) of th rusabl -wast to gt th following systm. " $ X S (P ) 0 # $ X D (P,P) 0 Th ffct of th disposal costs and th dgr of monitoring. dx dx dx dx dσ 0, as X is not a function of d, d S and σ. Likwis, dp dp dp dp dσ 0, as P is not a function of d, d S and σ. Th ffct of th rsal pric: (dx /dp and dp /dp) By taking th drivativ of th systm with rspct to P, w gt: # $ & dx dp S P * dp dp 0 dx dp D P * dp dp dd dp 0 and in matrix trm: # $ S P D P & ( # dx & ( ( # 0 & (* dp ( ( ( dp dd ( ( $ ( $ ' dp ' dp ' 22

25 W can thn calculat th acobian dtrminant as: S P D P D P + S P From th acobian dtrminant, w can dduc: 0 S P dx dp and dd dp D P 0 S * dd P dp with dd dp and S P dp dp D P dd dp Cas 2: Th non-rusabl -wast in th altrnativ -wast markt W also us th supply X 0 S 0 (P 0 ) and th dmand X 0 D 0 (P 0,P) of th non-rusabl -wast to gt th following systm. " $ X 0 S 0 (P 0,d ) 0 # $ X 0 D 0 (P 0,d S ) 0 Th ffct of th dgr of monitoring and th rsal pric. As nithr th quantity of th non-rusabl -wast nor its pric is a function of P and σ, w gt no ffct as follows. dx 0 dp dx 0 dσ 0 and dp 0 dp dp 0 dσ 0. Th ffct of th disposal cost d S in th South. Taking th drivativ of th systm with rspct to d S, w gt: 23

26 # dx 0 S 0 * dp 0 0 dd $ S dx 0 D 0 * dp 0 dd 0 0 & In matrix form w hav: # $ S 0 D 0 & # ( dx & 0 ( # 0 & ( dd (* S ( ( ( dp ( dd 0 ( 0 ( ' $ dd ( $ dd ( S ' S ' and S 0 D 0 D 0 + S 0 Thn w dduc: 0 S 0 dx 0 and dd 0 D 0 0 S 0 * dd 0 0 with dd 0 0 and S 0 dp 0 dd 0 dd 0 0 Th ffct of th disposal cost d in th orth. Th drivativ of th systm with rspct to d givs: # dx 0 S 0 * dp 0 ds 0 0 dd $ dx 0 D 0 * dp 0 0 & 24

27 In matrix form w hav: # $ S 0 D 0 & # ( dx & 0 ( # ds & ( dd (* ( 0 ( ( dp ( ( and 0 ( ( ' $ dd ( $ 0 ' ' S 0 D 0 D 0 + S 0 W dduc that: ds 0 S 0 dx 0 0 D 0 ds 0 * D 0 with ds 0 and D 0 0 and ds 0 dp 0 0 ds 0 0 Th ffct of th diffrnc in th disposal costs btwn th orth and th South (d - d S b) Th ffct on th quantity of th non-rusabl -wast is calculatd as follows. dx 0 db dx 0 * d S b + dx 0 * d b - dx 0 + dx 0 - S 0 * dd 0 ds 0 * D 0 W also dtrmin th ffct on th pric of th non-rusabl -wast. dp 0 db dp 0 * d S b + dp 0 * d b - dp 0 + dp! # if 0 " # $ dp 0 dp 0 0 othrwis 25

28 Cas 3: Th standard -wast markt In th cas of a standard -wast markt, w considr th supply X S (P,d,σ) and th dmand XD (P,P, d S,σ) of -wast that lads to th following systm. " $ X S (P,d,σ ) 0 # $ X D (P,P,σ,d S ) 0 Th ffct of th rsal pric P dx S dp * 0 dp P dp dx D dp dd * 0 dp P dp dp In matrix form: S dx 0 P dp * dd and D dp dp P dp W dduc : S D D + S 0 S dx dp dd dp D S * dd dp with dd dp and S and 0 dp dp D P dd dp 26

29 Th ffct of th disposal cost d in th orth. dx S dp ds * 0 dd P dd dd dx D dp * 0 dd P dd In matrix form : S dx ds P dd * dd D dp and 0 P dd W dtrmin: S D D + S ds S dx 0 D ds * D with ds and D 0 and ds dp 0 ds 0 Th ffct of th disposal cost d S in th South. dx S dp * 0 dds P dds dx D dp dd * 0 dds P dds dds In th matrix form : 27

30 S dx 0 P dd S * dd D dp dd S P dd S and th aconbian dtrminant is : S D D + S W dduc that : 0 S dx dd D S * dd 0 with dd 0 and S and 0 dp dd dd 0 Th ffct of th diffrnc in th disposal costs btwn th orth and th South (d - d S b) W dtrmin th ffct on th quantity of -wast as: dx dx S * d dx d + * db dd b dd b S dx dd - S S * dd dx P + - dd ds * D Th ffct on th pric of -wast is: 28

31 dp db dp * d S b + dp * d b - dp + dp " dp $ if # $ 0 othrwis Th ffct of th dgr of th monitoring σ Th drivativ of th systm givs: dx S dp ds * 0 dσ P dσ dσ dx D dp dd * 0 dσ P dσ dσ dp In matrix form : S dx ds P * d σ d σ D dp dd P dσ dσ and S D D + S W dduc that : ds dσ S P dd D ds D S dd * + * dx dσ P dσ P P dσ dσ with dd dσ, S, D 0 and ds dσ 0 ( dd dq 0; dσ dσ ) ; dx! 0 " dσ # and ds dσ dp dσ dd dσ dd dσ ds dσ 29