Modelling and analysis of international recycling between developed and developing countries

Transcription

1 Resources, Conservaton and Recyclng 46 (2006) 1 26 Modellng and analyss of nternatonal recyclng between developed and developng countres Peter J.H. van Beukerng a,, Jeroen C.J.M. van den Bergh a,b a Insttute for Envronmental Studes, Free Unversty, De Boelelaan 1087, 1081 HV Amsterdam, The Netherlands b Department of Spatal Economcs, Faculty of Economcs and Busness Admnstraton, Free Unversty, Amsterdam, The Netherlands Receved 20 January 2005; accepted 8 June 2005 Avalable onlne 2 August 2005 Abstract To deal wth the complexty of recyclng, a wde varety of models have been developed, each servng a specfc purpose. Despte the current trend ncreasng nternatonal trade n recyclng-related materal flows, the nternatonal dmenson of physcal and economc relatonshps n recyclng s often gnored n current models and analyses. Ths paper develops a formal model of an nternatonal materalproduct chan (MPC) that represents the mechansm behnd nternatonal recyclng. The attenton s focused on the case of a developed and a developng country that exchange materal commodtes, fnal products and recyclable waste. Among others, the model demonstrates that takng nto account envronmental externaltes results n hgher levels of recyclng. Moreover, we show that nternatonal recyclng s manly drven by regonal dfferences n the quantty and qualty of factor endowments and economc effcency of recyclng. Gven that ndustralsed countres are relatvely well endowed wth recyclable waste, the recovery rate usually exceeds the utlsaton rate. In developng countres, an opposte pattern s observed Elsever B.V. All rghts reserved. JEL classfcaton: F1; O1; Q3; Q53; Q56 Keywords: Foregn trade; Secondary materals; Waste polcy Correspondng author. Tel.: ; fax: E-mal addresses: beukerng@vm.vu.nl (P.J.H. van Beukerng), jbergh@feweb.vu.nl (J.C.J.M. van den Bergh) /$ see front matter 2005 Elsever B.V. All rghts reserved. do: /j.resconrec

2 2 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) Introducton To deal wth the complexty of recyclng, a wde varety of emprcal models have been developed, each servng a specfc purpose. All these models defne analytcal boundares,.e. no one model captures the complete system of economc and recyclng processes. Usually, the nternatonal dmenson of physcal and economc relatonshps behnd recyclng s gnored. Ths s not n lne wth the current trend of ncreasng nternatonal trade n secondary materals that end up beng recycled. For example, whle n 1970 only 15% of the recovered copper scrap was traded nternatonally, ths share grew to 48% n Smlar ncreases n the trade ntensty can be observed for waste paper and alumnum (Van Beukerng, 2001). The globalsaton of the recyclng market ncreases the need for analyss of the nternatonal materal-product chan (MPC) that captures the varous stages n the nternatonal lfe cycle of a materal or physcal product. The am of ths artcle s to develop a formal, two-country model that represents the basc economc mechansms behnd nternatonal recyclng. Subsequently, the model wll be analysed, where a comparson wll be drawn between a world wth recyclng n autarkc economes and one wth recyclng n the context of an nternatonal system of trade relatonshps. Although the model s farly general, the case of nteracton between a developed and a developng country wll be emphassed, as ths currently seems to be the domnant pattern n nternatonal recyclng (van Beukerng, 2001). The organsaton of the artcle s as follows. In Secton 2, the varety n approaches adopted by exstng appled models that deal wth (elements of) recyclng s examned. Secton 3 presents a conceptual model of nternatonal recyclng, and provdes a detaled dscusson of the varous elements t contans. In Secton 4, ths s translated nto a set of formal models of recyclng n autarkc and tradng economes, whch are subsequently analysed and compared. A fnal secton concludes. 2. Characterstcs of current recyclng models A revew of 31 emprcal quanttatve studes has been conducted to gan nsght nto the varety of elements that are potentally relevant n analysng nternatonal recyclng (see Table A.1 n Appendx A). The overvew llustrates the dversty of studes but should not be consdered as an exhaustve survey of emprcal-quanttatve, economc models of recyclng. 1 Gven the number of studes surveyed, however, t does provde a good ndcaton of the varety of approaches found n the lterature. Ths s reflected n four characterstcs, relatng to model objectve, system boundary, spatal-geographcal dmenson and temporal features. 1 Theoretcal economc analyses of recyclng nclude the followng. Kandelaars and van den Bergh (1997a) adopt a partal statc equlbrum framework. Dnan (1993) and Fullerton and Knnaman (1995) study recyclng wth theoretcal general equlbrum models. Dynamc models of recyclng are studed n Lusky (1975), van den Bergh and Njkamp (1994) and Kandelaars and van den Bergh (1997b). For the place of recyclng models n the broader lterature on economc models wth materal flows, see van den Bergh and Janssen (2004, notably chapter 2).

3 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) Objectves and model types Three types of recyclng models can be dentfed. (1) Physcal models such as Substance Flow Analyss (SFA) and Lfe Cycle Analyss (LCA) descrbe the materal flows or measure the mpact of materals and products on the envronment. They gnore economc, substtuton and dynamc aspects of materal flows (Kandelaars and van Dam, 1998). Because recyclng has been tradtonally treated as a techncal problem, physcal models seem to domnate: 14 out of 31 studes can be classfed as such. (2) Economc models, such as partal and general equlbrum models, analyse the relatonshp between the use of materals and economc varables but mostly gnore the envronmental mpact and substtuton between materals. Ten out of 31 studes are classfed as economc models. (3) Integrated models, such as the materal-product chan (MPC), are defned as a set of lnked flows of materals and products and cover the complete lfe cycle of a materal, often addressng mass balance explctly. Only 7 out of 31 studes can be classfed as ntegrated models. Recyclng models can also be classfed as descrptve and scenaro versus optmsaton models. Descrptve and scenaro models often nclude dynamc, causal relatonshps. Optmsaton models apply an optmsaton objectve and usually focus on statc relatons between varables. These models often allow substtuton between producton factors, such as captal, labour, energy and materals (Anderson, 1987). Seventeen out of the 31 studes are drven by optmsaton System boundares Recyclng s embedded n a chan of economc and physcal techncal processes and thus has potentally up- and down-stream effects. To address these, the vertcal and horzontal system boundares have to be determned wth care. The vertcal boundary follows from the choce of where n the lfe cycle to cut off the analyss. The horzontal boundary s the result of choosng between a focus on a sngle materal or product and takng nto account substtuton effects between dfferent materals (Kandelaars and van Dam, 1998). Usually, a dstncton s made between open- and closed-loop recyclng (Bogusk et al., 1994). Closed-loop recyclng s a process n whch the materal of a physcal product s recycled nto the same produce, a process that may-n theory-be repeated endlessly. Open-loop recyclng s a process n whch the (vrgn) materal of a product s recycled n a product that after use s dscarded. Open-loop recyclng provdes a more realstc representaton of most types of current recyclng (Fnnveden, 1999). For certan materals, however, closed-loop recyclng s a sutable form. For example, n the case of lead, lead-acd batteres are both the man source and destnaton of the recyclng process (Socolow and Thomas, 1998) Spatal-geographcal settng Wth the excepton of logstc studes, most analyses of recyclng tend to underestmate mportance of the spatal dmenson. Geographcal factors, however, often play a crucal role both wthn and outsde the focal area. Wthn the regon, for example, the populaton densty of the focal area determnes to a large extent the success of recyclng programmes. Moreover,

4 4 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 a regon may strongly depend on mports or exports of materals or materal resources. Of the 31 surveyed studes, 11 assume closed regons, 13 nclude elements outsde the regon n an exogenous manner and 7 studes allow elements outsde the regon to nfluence the processes n the focal area. Internatonal trade of secondary materals s growng rapdly. For example, whle n 1970 only 15% of the recovered copper scrap was traded nternatonally, ths share grew to 48% n Smlar ncreases n the trade ntensty can be observed for waste paper and alumnum (van Beukerng, 2001). To analyse nternatonal recyclng, t s mportant to separate recyclng nto waste recovery and utlsaton phases. After all, secondary materals that are recovered and exported by a country can no longer be utlsed by that country. In the survey, only 16 out of 31 studes clearly dstngush between the recovery and the utlsaton of recyclable waste. The spatal dmenson s not only mportant from the perspectve of economc trade of secondary materals. Envronmental problems may also cross borders,.e. envronmental externaltes may be of an nternatonal nature. Eder and Narodoslawsky (1999) propose a typology of a regon s responsblty for envronmental pressures, dstngushng responsblty for mpacts nsde and outsde the boundares of the regon. Hoekstra and Janssen (2002) propose a smlar approach n the context of tradng countres Temporal features Recyclng studes can be statc or dynamc n nature. Dynamc models allow to address changes n technology and demand, accumulaton of captal and polluton and tme lags n nvestment and R&D or n polluton mpacts on welfare. Only 9 of 31 surveyed studes have explctly addressed the temporal dmensons of recyclng. The specfc economc relevance of ncorporatng dynamc processes n models of recyclng systems vares wth the applcaton. For example, tme lags n recyclng processes take dstnct forms for dfferent materals (Grace et al., 1978). Most packagng materals have a lfetme of less than a year, whle constructon materals last more than 15 years. Tme lags may also be due to recovery and utlsaton. Recovery costs and commodty prces play an mportant role here. In addton, the physcal features of materals count. For example, organc waste cannot be stored for a long perod of tme, and therefore has to be composted wthout much delay. Car tyres, on the other hand, are often stored n monoflls for long perods of tme before beng recycled. Fnally, envronmental effects of (lack of) recyclng actvtes may also occur wth a delay. In analysng recyclng, the waste generaton rate per capta ncome s lkely to alter over tme, wth evdent consequences for waste plannng. Consumer preferences may change over tme, thus affectng sold waste generaton per capta or recyclng tself. For example, Pe and Tlton (1999) study the factors affectng the ncome elastcty of metal demand. Especally n developng countres demand s senstve to changes n ncome. Product lfe extenson s another factor that causes changes n the MPC. Postve economc and envronmental effects may result from t, due to lower levels of producton and dsposed waste. Negatve mpacts are also possble, due to use of more materals per unt of product or due to a phenomenon known as the vntage effect,.e. a lack of replacement of old, neffcent equpment (Conn, 1977; Navarett et al., 1998).

5 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) A conceptual model of the nternatonal materal-product chan Snce recyclng s strongly dependent on up- and down-stream processes, the most relevant segments of the nternatonal MPC should be ncluded n the analyss. These segments nclude the producton of prmary and secondary materals, the manufacturng of fnal products, the consumpton of these products and the management of sold waste. Second, nternatonal trade n varous parts of the MPC should be allowed. Ths trade can take place between dfferent segments (nter-ndustry trade) and between smlar segments (ntra-ndustry trade). Thrd, the most fundamental elements that affect recyclng n the MPC should be accounted for. Such model elements may nclude economc, envronmental, nsttutonal, dynamc and nternatonal aspects n each stage of the MPC. Fg. 1 presents a conceptual model of nternatonal recyclng that meets these requrements. Ths framework represents the MPCs of two hypothetcal countres A and B whch exchange of materal commodtes, fnal products and recyclable waste. Followng the sequence of the segments n the MPC, the most relevant model elements that nfluence the domestc and nternatonal movement of materal flows, are dscussed below. Specal attenton s pad to the dfferences n the MPCs between developed and developng countres Producton of raw commodtes In the producton stage of the MPC, prmary and secondary commodtes are prepared for the manufacturng stage. The most mportant factors n determnng the Fg. 1. A conceptual model of nternatonal recyclng.

6 6 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 Fg. 2. Model elements: producton of raw commodtes. level of recyclng n the raw commodty producton stage of the MPC are depcted n Fg. 2. As fnancal motves often form a strong ncentve for recyclng, the relatve costs and benefts of prmary and secondary commodtes predomnantly determne the nput choce of producers (Bower, 1977). The costs are determned by the purchase prce of the nputs and the addtonal factors requred to convert the materals nto commodtes. The benefts depend on the sellng prce of the commodtes to the manufacturers. Several dfferences exst between the secondary and the prmary commodty ndustry. Frst, the scale of operaton n the recyclng ndustry s generally smaller than n the prmary commodty ndustry. Second, prmary producton processes are generally energy and captal ntensve and requre lmted and hghly sklled labour, whle secondary processes consume relatvely lttle energy and are labour ntensve. Ths s why an ncrease n energy prces promotes materal recovery and utlsaton (Bower, 1977). Thrd, the secondary commodty markets are often clamed to be more volatle than prmary commodty markets (Yohe, 1979; Pearce and Grace, 1976). Ths s one of the reasons why recyclng ndustres operate on a smaller scale. Rsk-averse frms then refran from nvestng n recyclng actvtes (Butln, 1977). Fourth, the secondary ndustry s less envronmentally damagng than the prmary ndustry (Bartone, 1990). From an nternatonal perspectve, there are several dfferences between developed and developng countres n ths segment. Frst, the avalablty and costs of producton factors vary sgnfcantly. Developng countres are well endowed wth unsklled labour and prmary natural resources. Captal, sklled labour and secondary resources are the abundant factors n developed countres. Second, the shape of and the poston on the learnng curve n the ndustry dffers. Therefore, technologcal change s less easly accomplshed n developng countres. Hgh-transacton costs to swtch to alternatve, large-scale technologes prevent recyclng frms n the South from makng the change to these technologes. Instead, they tend to stck to technologes, whch they have already been usng for a long perod of tme (Navarett et al., 1998). A thrd dfference s relates to ths, namely that the scale of operatons n developng countres s generally smaller. A fnal dfference s that envronmental legslaton s less strct n developng countres, whch obvously wll affect waste management, trade n materals and recyclng.

7 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) Manufacturng of fnal commodtes Fnal commodtes are ntermedary products sutable to be drectly converted nto consumer goods (e.g. crude steel and Kraft paper). Most fnal commodtes can be produced from prmary and secondary commodtes. The crucal factors that determne the recyclng level n the manufacturng stage of the MPC are shown n Fg. 3. The choce to use secondary materals n the fnal commodtes depends on a number of factors. Frst, the substtutablty of prmary and secondary commodtes n the manufacturng process vares across materals. For example, newspaper can be made of both wood pulp and waste paper. Untl recently, wrtng paper could not use waste paper n ts manufacture because the latter s of lower qualty (Weaver et al., 1995). Second, manufacturers wll only choose secondary materals f constant qualty and quantty of supply s guaranteed. Secondary commodty nputs are generally of a more heterogeneous qualty than prmary materals. Therefore, there s a hgher rsk that the producton process wll malfuncton due to the low qualty of the nputs. Another source of uncertanty s the relatve nstablty of the secondary commodtes market, whch jeopardses the contnuty of the manufacturng process (van Beukerng and Bouman, 2001). Thrd, the nput choce has an effect on the envronmental mpacts of the manufacturng stage. From an nternatonal perspectve, varous factors need to be taken nto account. On the one hand, many developed countres have adopted legslaton to encourage or mandate the utlsaton of waste. Examples are mandated mnmum recycled materal content n selected products and government procurement practces that favour recycled materals. These polcy nterventons are uncommon n developng countres. Therefore, such product standards may create conflcts n nternatonal trade. On the other hand, manufacturers n the North are generally exposed to more strngent standards wth regard to the utlsaton of secondary materals. For example, t s strctly prohbted to use recycled materals n food packagng. Although smlar restrants apply to producers n many developng countres, the level of enforcement there s much lower. An addtonal aspect s the large mpact of transport costs of bulky fnal commodtes. Ths may dscourage the nternatonal trade of prmary and secondary products. Fnally, the labour costs are especally mportant n the manufacturng ndustry, whch s relatvely labour ntensve. Ths creates a comparatve advantage for manufacturng n developng countres. Fg. 3. Model elements: manufacturng of fnal commodtes.

8 8 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 Fg. 4. Model elements: consumpton of fnal products Consumpton of fnal products Consumers are mportant as customers of potentally recycled consumer products and as supplers of recyclable materals. Consumer products are fnal goods generated n the fnal producton (manufacturng) stage n the MPC before consumpton (e.g. cars and books). These products may contan both prmary and secondary commodtes. The most mportant factors n determnng the level of recyclng n the consumpton stage of the MPC are depcted n Fg. 4. The wllngness to recycle by consumers depends on a number of factors. Frst, consumers wth hgh-ncome levels are more lkely to voluntarly partcpate n recyclng programmes (Jenkns et al., 1999; Hong et al., 1993). Secondly, ths wllngness declnes f such recyclng s tme-ntensve (Godbey, 1996; Jenkns et al., 1999). Ths mples that tme and atttudes toward tme are crtcal varables n any attempt to understand changes n the generaton of muncpal sold waste from household sources. Fnally, the drect envronmental effect of consumng secondary products may be more pronounced due to the vntage effect and ther lower durablty. For example, the lfetme extenson of a product through ncreased reuse and recyclng often results n relatvely hgher energy consumpton levels because the technologcal mprovements are not emboded n reused products, such as cars and refrgerators. The nternatonal context plays a role n varous ways. Frst, hgh-wages are closely correlated wth strct envronmental regulaton and stronger envronmental awareness (Dasgupta et al., 1996; Man and Wheeler, 1998). Therefore recyclng s promoted more n hgh-ncome countres (Jenkns et al., 1999; Hong et al., 1993). The demand for nexpensve secondary products, however, s especally large n poor countres (van Beukerng, 1997). Secondly, cultural dfferences can have an mpact on the purchasng behavour of consumers. Kshno et al. (1999) show wth respect to purchasng behavour for tolet paper how Germans attach a hgher mportance to the envronmental aspects of the product than Japanese Management of sold waste and other resdues The MPC waste stage deals wth the management of sold waste and recyclable resdues. Sold waste comprses resdue materals that can no longer be converted nto useful materals

9 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) Fg. 5. Model elements: waste management of resdues. or products n an economcally feasble manner. Recyclable resdues are materals that are economcally sutable for recovery. The man factors that determne the level of recyclng n the waste management stage are shown n Fg. 5. A number of ssues are mportant to modellng ths segment. Frst, due to degradaton of products and materals, reuse and recyclng ultmately wll reach ther lmts. Then they should preferably be used for the generaton of energy ( thermo-recyclng ). Ths form of sequental explotaton of the full potental of a resource s consstent wth the noton of resource cascadng (Srkn and Ten Houten, 1993). Second, scale effects are relevant n the waste management stage. For example, a hgher level of waste generaton (per capta) allows for a hgher effcency of recovery (van Beukerng and Bouman, 2001). Also the composton of waste from hgh-ncome households allows for a hgher degree of recovery (Chang and Ln, 1997). Smlar scale effects apply to waste collecton and the operaton of landflls and ncnerators (Palmer et al., 1997). Thrd, because waste management servces are tradtonally not market drven, government legslaton and ts enforcement are crtcal to development of waste management and recyclng. The exstng type of nfrastructure and recovery system often restrcts future developments. In the Netherlands, for example, sgnfcant nvestments have been made n ncneraton capacty, as a result of whch t s economcally unattractve to swtch to other types of waste management n the short-run. The nternatonal context plays a role n the followng ways. Frst, dfferences n legslaton determne the drecton and volume of certan materal flows. For example, nternatonal dfferences n the dsposal fee make t worthwhle to export waste materals as recyclable commodtes, whereas n realty these flows are destned for dsposal (Rosendorfová et al., 1998). Second, despte potental economc gans from trade, varous nternatonal agreements, such as the Basel Conventon, prohbt the nternatonal trade of certan hazardous recyclable materals. Thrd, especally n developng countres the exstence of an nformal recovery sector allows for large levels of recyclng. In developed countres, the recovery sector s formally organsed and often subsdsed. Fnally, the types of nstruments used dffer between countres. Developed countres ncreasngly use economc nstruments to motvate households to mnmse waste generaton. In developng countres the admnstratve capacty s lackng to mplement such polces.

10 10 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) A formal model of nternatonal recyclng To demonstrate the essental features and mplcatons of the nternatonal dmenson n recyclng, a smple analytcal model s developed. The model s of a statc nature as s common n the lterature on nternatonal trade theory. Ths mples that stocks are constant. As a result, the model s less sutable to address ssues surroundng precous materals lke slver and gold. The assumpton s, however, not overly restrctve when descrbng recyclng markets for certan bulky secondary materals, such as waste paper. Here, accumulaton of stocks, f relevant at all, always s a short-run phenomenon and thus never has a structural character. The model s developed n two steps. Frst, n Secton 4.1, a two-regon onemateral one-product model wth recyclng s presented, where no trade between the regons s allowed. The resultng model represents a sort of autarkc MPC. Next, Secton 4.2 extends ths to a model that allows for trade n prmary commodtes, recyclable waste and fnal products. Ths model represents an nternatonal MPC wth recyclng. The two regons represent hgh-ncome developed (ndustralsed) countres (c) and lowncome (developng) countres (dc). Ths dstncton s appled as both regons reveal very dfferent trade and recyclng features. The dstncton between the two regons n the model s based on dfferences n factor endowment of labour and prmary and secondary resources. Developed countres are well endowed wth secondary (recyclable waste) resources, captal and hghly sklled labour. Developng countres are well endowed wth prmary resources and unsklled labour, whle lackng captal. The developed countres therefore have a comparatve advantage n the producton of secondary commodtes and the manufacturng of products from prmary commodtes. The developng countres have a comparatve advantage n producng prmary commodtes and manufacturng fnal products from secondary commodtes. The optmal confguraton of trade n secondary materals results from the mnmsaton of socal costs at the system s level. The prvate costs are determned by the use of a number of producton factors consstng of labour (L ), captal (K ) and extracted materal (E ). The costs for these producton factors are p L, p K and p E. Besdes the prvate costs of these producton factors, external costs are caused by the non-recycled waste flows (W). The costs of these external effects are denoted as p W. The defned prces dffer between the regons. The optmsaton process s conducted under two condtons. The frst s that the prvate costs are mnmsed. Prvate costs consst of the accumulated costs for labour, captal and materals. The second condton s that the socal costs are mnmsed. The socal costs are the sum of the prvate and the external costs. External costs are the costs related to usng the producton factor envronment. Fg. 6 llustrates a stuaton n whch the nternalsaton of external costs shfts the recyclng equlbrum n a country. The x-axs (0D) presents the fxed demand, whch can be satsfed by prmary and secondary materals. Readng from left to rght, the left y-axs depcts net benefts of the consumpton of secondary materals. Readng from rght to the left, the rght y-axs represents the net benefts of the consumpton of prmary materals. Two negatvely sloped net beneft functons have been drawn. Increased consumpton of prmary materals results, for example, from ncreased scarcty, whch requres more extracton effort and thus hgher costs. Increased consumpton of secondary materals leads to

11 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) Fg. 6. Externaltes of vrgn and secondary producton. lower net benefts because, for example, a hgher degree of recovery generally results n a lower qualty of the recovered materals. Both margnal beneft curves ntercept the horzontal axs. Ths ndcates that, beyond a certan degree of prmary or secondary utlsaton, margnal costs exceed the margnal benefts. In a stuaton, where the optmal materal confguraton s based on prvate costs only, the allocaton of nputs s determned at R prvate, where the margnal benefts of prmary and secondary materals concde. In ths equlbrum, the overall demand s satsfed by an amount of 0R prvate of secondary materals and an amount of R prvate D of prmary materals. Due to nternalsaton of external costs, the recyclng equlbrum wll shft. In ths case, t s assumed that both the producton of prmary and secondary materals generate negatve externaltes. Negatve effects of secondary materals may result from potental health mpacts on waste recovery workers. Negatve effects of prmary materals may result from the ncreased rate of depleton of natural resources. Therefore, the socal net beneft curves for both materals le below the prvate net beneft curves. Externaltes of prmary materals are larger than for secondary materals. In the new stuaton, the equlbrum shfts n favour of recyclng (from R prvate to R socal ). The amount of secondary materals ncreases from 0R prvate to 0R socal. If negatve externaltes of recyclng domnate, however, a shft n the opposte drecton may occur The autarkc materal-product chan Here, we frst present a model of the MPC for a two-country world under autarkc condtons. The two regons represent ndustralsed or developed countres (c) and developng countres (dc). The regons dffer n terms of factor prces, factor endowment for prmary

12 12 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 resources, per capta demand and economc effcency n varous stages of the MPC. No nteracton occurs between the regons. The model descrbes nteracton of physcal and monetary dmensons, both coverng the full lfe cycle of the materal. The producton factor dmenson s exogenous,.e. not made dependent on the economy: t only serves as a source of factor and resource nputs n the MPC. Changes n the producton factors dmenson nfluence the physcal dmenson through the monetary dmenson. (Note that regons are denoted as superscrpts and segments (stages n the MPC) are denoted by subscrpts). The statc nature of the model mples exogenous process technques. At the begnnng of the MPC, a prmary resource s extracted and processed nto a prmary commodty n the prmary producton segment (P). The secondary resource that s retreved from the dscharged waste flow s processed nto a secondary commodty n the secondary segment (S). Both commodtes are transformed nto fnal products n the manufacturng segment (Q). Ths manufacturng process satsfes the exogenous demand (D). After consumpton, the fnal products are ether dscarded to the waste management segment (W), or separated and suppled to the waste recovery segment (R). In the latter stage, the recyclable waste s cleaned and suppled to the secondary commodty segment. The producton of P, S and the manufacturng of Q generate non-recycled waste as a by-product. These are denoted by W P, W S and W Q, respectvely. The producton factor dmenson s exogenous. The stocks and prces of the factors: extracted resources (E), captal (K) and labour (L), are gven. In other words, the MPC s a partal equlbrum model: the clearng of factor markets s not part of the optmsaton process. Labour costs (p L ), captal costs (p K ) and resource costs (p E ) are appled to transfer the physcal requrement for labour, captal and resources nto monetary unts. Labour, captal and waste are applcable for all segments n the MPC. Resources are only accounted for n the prmary materals sector, whch converts extracted resources (E) nto prmary materals (P). The external costs are drven by the amount of the non-recycled waste (W). Ths flow s accounted for by a prce per physcal unt of waste (p W ), whch represents the envronmental damage that s caused by the non-recycled waste. Examples of such envronmental damage nclude, for example, groundwater polluton resultng from effluent leakage from landflls or health damage caused by ar pollutants emtted by waste ncnerators. Extracted resources, materals and waste flows are expressed n tonnes, captal n peces of equpment and labour n number of workers. The monetary dmenson of the model covers accountng for the costs of the producton factors and the non-recycled waste. A global planner determnes the optmal confguraton of the autarkc MPC wth the am of mnmsng the total costs (TC) of satsfyng demand n both regons (). The control varables of the global planner are the prce of waste (p W ), and the prmary resources (p E ). The objectve functon s formulated as: mn TC = {c,dc} j {Q,P,S,R,D} p L L j + p K K j + p E E j + p W W j (1) Here, u denotes the utlsaton rate and r the the recovery rate (these wll be formally defned later on). The defnton of the total costs (TC) vares, dependng on the decson perspectve of global plannng. Frst, the planner can base the decson on prvate costs (PC), only. In ths prvate objectve functon, the cost of usng the producton factor waste (p W )

13 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) s assumed to be zero: PC = {c,dc} j {Q,P,S,R,D} p L L j + p K K j + p E E j (2) Secondly, the global planner can nternalse the external costs n the decson framework. In ths case, the cost of non-recycled waste (p W ) as denoted n Eq. (1) s not equal to zero. In ths polcy perspectve the decson s based on the socal costs rather than on the prvate costs. EC = p W W j (3) {c,dc} j {Q,P,S,R,D} In the followng, the basc relatonshps n the model are explaned. The model s drven by exogenous demand for a physcal commodty n both regons, expressed n tonnes: D = D for = c, dc (4) In lne wth realty, the demand n developed countres exceeds the demand n developng countres: D c >D dc (5) Because the number of households n both regons s equal, the per capta consumpton n ndustralsed countres exceeds the per capta demand n developng countres. As has been shown n Eq. (12), ths dfference s relevant for the effcency of the recovery sector (R), because ths sector generates economes of scale. The output of manufacturng (Q) satsfes the demand: D Q for = c, dc (6) Manufacturng segment Ths sngle product type can be manufactured from two types of materals (M): prmary and secondary materals (P and S). In addton, labour and captal are requred for the manufacturng of the product. The qualty of S s nferor to the qualty P,.e. manufacturng a certan amount of product wth only one type of materal requres more secondary materal (S) than prmary materal (P). For example, n addton to fllng materals the producton of 1 tonne of wrtng paper requres only 0.9 tonne of wood pulp. The same product based on recycled materals requres 1.2 tonne of waste paper. Obvously, n realty also a combnaton of waste paper and wood pulp can be used to produce paper. The qualty ndcator of materals (ε) denotes the effcency dfference of usng S versus P. The manufacturng process also generates a certan amount of non-recyclable waste (W q ). The producton functon of the manufacturng process s defned as: Q = f Q (M Q,K Q,L Q ) for {c, dc} = f Q (P + S /(1 + ε ),K Q,L Q ) (7)

14 14 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 Secondary materals (ε) n ndustralsed countres have an equal or better qualty than secondary materals n developng countres. ε c ε dc (8) Producton segment In the producton segment of the MPC, prmary and secondary materals are produced. The producton factors determne the producton of prmary materals. The stock of extracted resources avalable n the regon (E ) constrans the producton of prmary materals. Waste of resources n the prmary producton process s ndcated by τ. For example, for the producton of one tonne of prmary alumnum roughly 2.5 tonnes of bauxte are requred. Therefore, 1.5 tonnes are lost as non-recyclable waste. The prmary producton process generates a certan amount of non-recyclable waste (W p ). The producton functon of the prmary materals s defned as: P = fp (E /(1 + τ ),KP,L P ) for {c, dc} (9) In general, developng countres are better endowed n natural resources than ndustralsed countres. Therefore, the qualty of prmary resource materals n developng countres s assumed to be hgher than prmary materals n ndustralsed countres: τ c >τ dc (10) The producton of secondary materals (S) from recovered materals (R) s dependent on the qualty of the recyclable waste. The lower the qualty of the recyclable waste, the hgher s the effcency loss durng the secondary producton process. Ths effcency loss s ndcated by ϕ. The nterpretaton of ϕ s smlar to τ. For example, ndustral plastcs waste s generally more recyclable than household plastcs waste because t s less contamnated and more homogeneous. The secondary producton process generates a certan amount of non-recyclable waste (W s ). The producton functon of secondary materal s defned as: ( S = fs R ) (1 + ϕ ),KS for {c, dc} (11),L S The secondary materal effcency losses n developng countres are larger than the effcency losses n ndustralsed countres: ϕ dc >ϕ c (12) Producng 1 tonne of prmary materals generates more non-recyclable waste than producng 1 tonne of secondary producton: W P P > W S S for {c, dc} (13) Waste management and recovery segment In the waste management and recovery segment, post-consumed products are converted nto recyclable waste (R) and nto non-recyclable waste (W), whch s landflled or

15 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) ncnerated. The processng of post-consumed products (D) nto non-recyclable waste (W) requres captal and labour. D and W are expressed n tonnes. In the recovery process, recyclable waste (R) s retreved from post-consumed products (D). In the recovery process the factors labour and captal are requred. Economes of scale apply to the recovery sector. The larger the demand per capta, the less producton factor s requred to recover one tonne of recyclable waste: R = fr (D,KR,L R ) for {c, dc} (14) Materal balance condtons Varous materal balance condtons can be derved. These condtons are expressed n tonne. The materal balance for the manufacturng process s defned as: Q = P + S W Q for {c, dc} (15) A fxed porton of materal loss (W P ) occurs durng the prmary producton process: W P = E P for {c, dc} (16) A fxed porton of materal loss (W s ) occurs durng the secondary producton process: W S = R S for {c, dc} (17) The total amount of dsposed waste (W) s the porton of consumpton that s not recovered (D R) and the non-recyclable waste generated by the prmary and secondary materals sector (W P and W S ) and the manufacturng sector (W Q ). Although n realty a certan share of the producton and manufacturng waste s recyclable, these recyclable materals are assumed to be processed nternally and therefore are not treated separately. W = D R + W P + W S + W Q for {c, dc} (18) Indcators Several ndcators present the results of the optmsaton processes. The most mportant ndcators are the utlsaton rate (u ) and the recovery rate (r ). The utlsaton rate (u )s the share of secondary materals (S) used n the manufacturng of fnal products (Q): u = S Q for {c, dc, world} (19) The recovery rate (r ) s the amount of secondary materals recovered after consumpton, (R) as a share of the fnal demand (D): r = R D for {c, dc, world} (20) The optmal value of these ndcators wll be determned by solvng the optmsaton model. These values are between 0 and 1, as the maxmum percentage that can be utlsed or recovered s 100%: 0 u,r 1 for {c, dc, world} (21)

16 16 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 In the followng several model-based results are presented Result 1: snks and sources Substtutng (6), and the materal balance condtons (15) (17) n (18) gves: W = D R + E P + R S + P + S Q = E for {c, dc} (22) Ths mples that n a closed economy the total amount of non-recycled waste s exactly equal to the total amount of prmary resources extracted n that regon. In other words, what goes n must eventually come out. Note that ths result crucally depends on the statc nature of the model, not allowng for emboded materals n captal goods Result 2: the relaton between the utlsaton and the recovery rate Substtutng (6) and (17) n (19), t follows that: u = (R WS ) D for {c, dc, world} (23) and substtutng (20) n (23) gves u = r WS D for {c, dc} (24) Ths mples that f the recyclng sector s perfectly effcent (W S = 0) and the economy s closed, the utlsaton rate (u ) equals the recovery rate (r ). In other words, n a closed economy dscrepancy between u and r s fully determned by wastes n the recyclng sector. The hgher W S the less secondary materals are produced mplyng a lower utlsaton rate Result 3: factor productvty Eqs. (1) (12), (14) and (22) mply optmsaton of the followng Lagrangan: L = (p L L j + p K K j ) + { W (p E + p W )W + λ [f Q f } p 1 + τ,k P,L P j + 1 { } ] ε f 1 + ϕ f (D,KR,L R ),K S,L S,KQ,L Q D (25) where c, dc and j P, S, W, R, Q, wth λ shadow prces of constrants. Based on (25), margnal condtons can be derved about optmal factor and producton levels wthn the autarkc MPC. From the condton: L F = 0 (26) Q follows p L p K = f Q / L Q f Q / K Q (27)

17 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) Ths equaton shows that the relaton between the optmal use of labour and captal n the manufacturng sector (Q). These are standard equatons of factor prce ratos, whch equal ratos of relatve margnal productvty of factors. Smlar condtons hold for all combnatons F = K, L, W for = 1, 2 and all segments: prmary materals (P), secondary materals (S) and waste recovery (R). Note that the prce of W s p E + p W, followng from (22) (see (25)) Result 4: factor allocaton between the segments n the MPC Cross-allocaton of the homogenous factor captal (K) among the varous segments n the MPC s based on the followng relatons: L K Q = p K + λ f Q KQ = 0 (28) L K P = p K + λ f Q M Q f P K P = 0 (29) L K S = p K + λ 1 + ε fq fs MQ KS = 0 (30) L K R λ = p K + (1 + ε)(1 + ϕ) f Q M Q fs fr R KR = 0 (31) Combnng (28) and (29) results n: f Q K P = f Q f E f P K P (32) Ths mples that the drect margnal contrbuton of captal to the manufacturng of fnal products (Q) s equal to ts ndrect margnal contrbuton va the producton of prmary materals and ts contrbuton to fnal product manufacturng. Combnng (29) and (30) results n: f P / K P f S / K S = ε (33) mplyng that the drect margnal contrbuton of captal to the producton of prmary materals (P) s equal to the ndrect margnal contrbuton of captal va the producton of secondary materals. Reflectng the relaton M Q = P + S/(1 + ε) as shown n (7), ths equaton shows the contrbuton of captal allocated to ether processes, gven the contrbutons of prmary and secondary materals to total materals n the manufacturng process. The hgher the materal loss n manufacturng due to the use of secondary materals (ε) the more captal wll shft from the recyclng sector (S) to the prmary sector (P).

18 18 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 Combnng (28) and (30) results n: f S KS = 1 fs fr 1 + ϕ R KR (34) Ths mples that the drect margnal contrbuton of captal to the producton of secondary materals (S) s equal to ts ndrect margnal contrbuton va the recovery of waste (R) and ts effect on the producton of secondary materals. The hgher the effcency loss durng secondary producton (ϕ), the more captal shfts away from the recovery sector Result 5: nternalsaton of external costs The optmsaton results so far do not dstngush between prvate and socal costs. The external costs are presented by p w. In the followng, the cross-allocaton of the factor captal (K) between the varous segments n the MPC s based on the socal costs, n whch the external costs are ncluded: L W = p R + p W + λ fq fp 1 + τ M W = 0 (35) Combnng (31) and (35) results n: p K p R + p W = 1 + τ fs f R R KR (1 + ε )(1 + ϕ (36) ) fp W Ths mples that hgher external costs shft captal away from the dsposal sector towards the recovery sector Result 6: regonal specalsaton In the present model, the allocaton rules of the producton factors (L, K and E) are ndependent of the qualty ndcator of secondary materals n the manufacturng process (ε), the effcency loss durng the secondary producton process (ϕ) and the resource loss n the prmary producton process (τ). If all functons (f Q, f P, f S, f D and f R ) are dentcal between the regons and f we assume equal factor allocatons between the regons then the followng relatons hold (see (22)): W c = W dc = W = E (37) R c = R dc = R (38) Combnng these wth (10) and (12) gves E 1 + τ c < E 1 + τ dc (39) R 1 + ϕ c > R 1 + ϕ dc (40) Ths mples that developng countres retreve a larger share of ther requred materals from extracted prmary resources whle ndustralsed countres tend to focus more on the

19 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) recovery of secondary materals. Equal allocaton rules, however, do not necessarly mply equal allocaton proportons. Therefore, (39) and (40) have been adjusted, although t s rather unlkely that sgn reversal wll occur. Moreover, producton functons are not dentcal n ndustralsed and developng countres. Due to the slow rate of dffuson of technologcal nnovatons from ndustralsed to developng countres, the producton functons are more effcent n the former regons. Ths n turn leads to a renforcement of nequaltes n (39) and (40). Combnng (9) and (39) gves: P c <P dc (41) Ths mples that gven the current dfferences n effcences, developng countres specalse n the producton of prmary materals. Combnng (11) and (40) results n S c >S dc (42) whch means that ndustralsed countres specalse n the producton of secondary materals The nternatonal materal-product chan Next, the autarkc MPC s extended to an nternatonal MPC. Internatonal trade s allowed for prmary commodtes (P), recyclable waste materals (R) and fnal products (Q). The domestc relatonshps reman unchanged. The producton factors are assumed to be mmoble and the optmsaton rules as descrbed for the autarkc MPC stll hold for the nternatonal MPC. The man dfference s the ncreased flexblty of the ndvdual segments n the MPC to retreve nputs and market ther outputs. Ths may lead to an alternatve confguraton of the prmary and secondary materal flows, and thus a change n the utlsaton and recovery rate n the respectve MPCs n ndustralsed and developng countres. Moreover, the prvate, external and socal costs are lkely to change. The nternatonalsaton of the MPC only refers to certan materal flows. The producton factors captal and labour are assumed to be mmoble between the two regons. Therefore, besdes the changes n the materal elements, the producton functons reman the same n the open economes. Moreover, Results 3 and 4 reman the same. The man changes n the set of equatons representng the nternatonal MPC are the materal balance condtons. Therefore, only the latter category of equatons s presented n ths secton. It should be kept n mnd, however, that materal balance equatons only represent the consequence of the nternatonalsaton of the MPC. The causes of changes n materal flows are the factor prces and factor endowments n ndustralsed and developng countres. All materal balance equatons are expressed n tonnes Internatonal materal balance condtons Many of the relatonshps specfed n Secton 4.1 reman the same. Eq. (6) s replaced by (43). Domestc demand n both regons can be met through domestc and mported fnal products. The demand s defned as: D = Q Q exp + Q mp for = c, dc (43)

20 20 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) 1 26 Eq. (44) replaces (15). The manufacturng process n both regons consumes domestc and mported prmary materals and domestc secondary materals. Trade of secondary materals s assumed to be non-exstent. The manufacturng of fnal goods n ndustralsed and developng countres s defned, respectvely, as: Q = P P exp + P mp + S W Q for = c, dc (44) In realty, processng of extracted resources nto prmary materals s conducted n the same country to avod excessve transport costs and to ncrease the value added of that resource. Therefore, prmary materals are assumed to be produced from domestc resources only. Eq. (45) replaces (17). Secondary materals are produced from domestc and mported recyclable waste. Materal waste (W S ) occurs durng the secondary producton process. S = R R exp + R mp W S for = c, dc (45) In accordance wth nternatonal legslaton, trade of non-recyclable waste s assumed to be prohbted. Therefore, the materal balance for the waste management process s smlar to that of the domestc MPC represented n (18). Dsposed waste s the sum of non-recovered consumer waste, non-recyclable waste from prmary and secondary materals sectors and manufacturng: W = D R + W p + W s + W q for = c, dc (46) Assumng the p W to be zero, thereby gnorng the external effects caused by non-recycled waste, the materal balance restrctons of the nternatonal MPC allows the dervaton of the several materal balance condtons Result 7: open snks and sources By substtutng (43), (44), (16) and (45) n (46), t follows that: W = E + (R mp R exp ) + (P mp P exp ) + (Q mp Q exp ) for {c, dc} (47) Ths replaces (22). The obvous concluson from ths result s that n an open economy the total amount of non-recycled waste s determned by the total amount of prmary resources retreved n that regon plus the trade balance n physcal terms for the other trade channels n the MPC. Result 1 n (22) s thus extended wth a trade dmenson for recyclable waste, prmary materals and fnal products Result 8: the nternatonal relaton between the utlsaton and the recovery rate Substtutng (19) and (20) n (45) gves: u = r D Q + R mp R exp Q W S Q for {c, dc} (48) Ths replaces (24). Note that f D = Q then t reduces to (24). The result n (48) mples that f the economy s open, the utlsaton rate (u ) no longer automatcally equals the recovery rate (r ). In an open economy, dscrepances between u

21 P.J.H. van Beukerng et al. / Resources, Conservaton and Recyclng 46 (2006) and r are determned by (1) the trade balance of the fnal products (D/Q); (2) the trade balance of recyclable waste (R mp R exp ); (3) the neffcences n the domestc recyclng ndustry (W s ). The more a country s charactersed as a net-mporter of fnal products (D > Q), the more lkely t s that the utlsaton rate exceeds the recovery rate (u > r). Lkewse, the more a country s charactersed as a net-mporter of recyclable waste, the more lkely t s that the utlsaton rate exceeds the recovery rate (u > r). Fnally, the more neffcent the recyclng sector s n processng secondary materals from recyclable waste, the fewer secondary materals become avalable for utlsaton n fnal producton. Therefore, n countres wth large neffcences n the recyclng ndustry (W s ), the recovery rate tends to exceed the utlsaton rate (r > u) Result 9: factor productvty and allocaton n an open economy If we substtute (47) n (25) then solvng gves the condtons for an optmum n the open economy wth trade. Results (26) (36) reman the same. In addton, we have: f Q P exp = f Q P mp (49) f S R exp = f S R mp (50) Eq. (49) means that n the optmum the margnal effect of prmary mports and exports on manufacturng output need to be equal. Smlarly, (50) states that n the optmum the margnal effect of mports and exports of recovered materals on the output of secondary materals producton needs to be equal. These condtons restrct the flows of mports and exports of prmary and secondary materals across countres Result 10: nternalsaton of external costs n an open economy Addtonal results are based on L/ X = 0 for X = R mp,r exp,p mp,p exp,q mp,q exp cf. (36), one set of addtonal condtons s of the form: p K p E + p W = 1 + τ fs f R R KR (1 + ε )(1 + ϕ ) f P E E X (51) wth X takng values as ndcated above. Here, E/ X = 1 for X = W,R mp,p mp,q mp and E/ X = 1 for X = R exp,p exp,q exp. Ths mples that hgher external costs assocated wth waste shft captal away from dsposal to recovery. In addton, t shows that such hgher external costs stmulate exports of waste, manufactured output and prmary resources, whle they have a negatve mpact on mports of these. Ths relatonshp can s clearly vsble n the waste market n ndustralsed countres. Hgher external costs of sold waste have led to ncreased waste recovery and expanson of the waste exports.