Envronment and Development Economcs 11: 371 391 C 2006 Cambrdge Unversty Press do:10.1017/s1355770x06002853 Prnted n the Unted Kngdom Survvng from garbage: the role of nformal waste-pckers n a dynamc model of sold-waste management n developng countres ROCÍO DEL PILAR MORENO-SÁNCHEZ Insttuto de Investgacón de Recursos Bológcos Alexander von Humboldt, Bogotá, Colomba. E-mal: rpmoreno@humboldt.org.co JORGE HIGINIO MALDONADO Department of Economcs at Unversdad de los Andes, Bogotá, Colomba. E-mal: jmaldona@unandes.edu.co ABSTRACT. In developng countres, nformal waste-pckers (known as scavengers) play an mportant role n sold waste management systems, actng n a parallel way to formal waste collecton and dsposal agents. Scavengers collect, from the streets, dumpstes, or landflls, re-usable and recyclable materal that can be rencorporated nto the economy s producton process. Despte the benefts that they generate to socety, waste-pckers are gnored when waste management polces are formulated. The purpose of ths paper s to ntegrate the role of scavengers n a dynamc model of producton, consumpton, and recovery, and to show that, n an economy producng sold waste, effcency can be reached usng a set of specfc and complementary polces: a tax on vrgn materals use, a tax on consumpton and dsposal, and a subsdy to the recovery of materal. A numercal smulaton s performed to evaluate the mpact of these polces on landfll lfetme and natural resource stocks. A dscusson on the mplementaton of these nstrumentssalsoncluded. Introducton In both developed and developng countres, populaton growth, as well as producton and consumpton patterns, has ncreased rates of sold waste producton, creatng constrants on the mprovement of human envronmental and health condtons. These constrants are aggravated n the developng world by lack of envronmental controls on ndustral processes, and nadequate or nsuffcent facltes for waste management and treatment (Ojeda-Benítez et al., 2002). In several developng countres, a sgnfcant proporton of the urban poor are nvolved n waste collecton and recyclng as a source of ncome. The authors are especally grateful to Darrell Hueth, who has accompaned and supported ths study snce ts begnnng. We also thank Ian Sheldon, and the EDE anonymous revewers for ther suggestons and helpful comments.
372 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado They are known as scavengers or waste-pckers. Ths actvty benefts socety as producton costs n some sectors are reduced and landflls lfetme s lengthened. In addton, vrgn materals are less ntensvely used, ncreasng the avalablty of natural resources. The purpose of ths paper s to show that scavengers n developng countres generate a postve externalty to socety (lengthenng of empty landfll space and natural resources avalablty) and, therefore, ther actvty should be encouraged through economc ncentves that lead them to ncrease the amount of sold waste recovery up to economcally effcent levels. The role of waste-pckers s ncorporated n an ntegrated dynamc model of producton, consumpton, dsposal, and recyclng of waste. The frst part of the model nvolves the nter-temporal maxmzaton of a socal welfare functon, whch depends on consumpton and an envronmental qualty ndex, constraned by evoluton functons for the stock of empty landfll space and natural resources used n the producton of commodtes. In the second part, a dynamc compettve equlbrum scenaro s constructed for each of three groups of agents, producers, consumers, and waste-pckers, and optmalty condtons are derved for each group. The condtons for socal optmalty are then compared wth the compettve equlbrum condtons, n order to derve the set of economc nstruments needed to reach effcency n resource allocaton, ncludng empty landfll space, n a market economy. The results of ths paper show that effcency n ths economy of producton, consumpton, waste dsposal, and recyclng requres the mplementaton of a set of optmally targeted polces workng smultaneously rather than a sngle polcy. A polcy amed at recognzng the actvty of waste-pckers n developng countres s part of the necessary set of nstruments requred for effcency. Numercal analyss s then developed to llustrate the mplcatons of the model. A dscusson on the mplementaton of these polces s also ncluded. Background The physcal characterstcs of ctes n developng countres, ther rapd expanson, and the lack of resources to provde for necessary nfrastructure and urban servces translates nto an nsuffcent collecton of waste generated, as well as ts mproper dsposal on the streets, vacant lots and, at best, n muncpal open dumps. Despte spendng 30 to 50 per cent of ther operatonal budgets on waste management, authortes n developng countres only collect between 50 and 80 per cent of the refuse generated, leavng, n some cases, a sgnfcant porton of the populaton wthout access to waste collecton servces. Systems for transfer, recyclng and/or dsposal of sold waste are unsatsfactory from an envronmental, economc, and fnancal pont of vew (Bernsten, 1993; Schubeler, 1996). Urban sold waste management n developng countres comprses both formal and nformal sectors. The formal sector conssts of muncpal agences or prvate frms that are responsble for waste collecton, transport, and dsposal. The nformal sector comprses unregstered, unregulated actvtes carred out by ndvduals, famles, groups, or small enterprses.
Envronment and Development Economcs 373 It ncludes several actors such as waste-pckers, tnerant buyers, small scrap dealers, and wholesalers. Householders also contrbute nformally to recyclng by engagng n source separaton n a lmted way (Sudhr et al., 1996). An mportant characterstc of nformal waste recovery and recyclng n developng countres s the partcpaton of waste-pckers. These selfemployed workers are also called scavengers, recyclers, or rag pckers, although they receve other names dependng on the local language, the place they work, and the materals they collect (Medna, 1997). Snce such waste recovery s labor ntensve, t provdes a lvelhood for many new mmgrants and margnalzed people n metropolses whose basc motvaton s ncome generaton (Ojeda-Benítez et al., 2002). Scavengng s assocated wth hgh unemployment, wdespread poverty, and the lack of a safety net for the poor. As stated by Medna (2001), n tmes of war or severe economc crses, scavengng ncreases wth partcular ntensty. In some cases, nformal waste workers belong to relgous, caste, or ethnc mnortes, and socal dscrmnaton s a factor that oblges them to work under completely unhygenc condtons as waste collectors or sweepers. Ther assocaton wth an actvty, whch the publc perceves to be flthrelated, tends, at the same tme, to perpetuate dscrmnaton aganst them. Informal waste workers usually lve and work under extremely precarous condtons; scavengng, n partcular, requres very long workng hours and s often assocated wth homelessness. Besdes socal margnalzaton, waste workers and ther famles are subject to economc nsecurty, health rsks, lack of access to normal socal servces such as health care and schoolng for chldren, and the absence of any form of socal securty (Schubeler, 1996). Waste-pckers can be classfed nto two groups, accordng to the place where they collect recyclables: dump waste-pckers and tnerant wastepckers. Dump scavengers lve ether on or besde landflls n order to awat the arrval of waste flled trucks. Itnerant scavengers collect recyclables on the streets, near the source, before waste s transported to the dump or landfll. Commonly, waste-pckers do not have access to adequate equpment and storage places, sortng the garbage wth ther bare hands, stcks, or smple hooks, and thus they are exposed to publc and envronmental health hazards (Kaseva and Gupta, 1996; Medna, 2000; Ojeda-Benítez et al., 2002). The exstence of scavengng s based on the presence of markets for recovered materals; waste n suffcent quantty and qualty to meet ndustral demand; and people wllng or compelled to do work that s poorly pad, hazardous, and of a low status (Hogland and Marques, 2000). The contrbuton of waste-pckers n developng countres s dffcult to quantfy due to the nformal nature of ths sector. Nonetheless, there are well-recognzed envronmental, economc, and socal benefts assocated wth scavengng actvty: Recyclng of sold waste reduces ar and water polluton, saves energy, reduces waste from ndustral processes compared wth the use of vrgn materals, and n many cases reduces mports of raw materals (Johnson et al., 1984; Medna 1997; Medna, 2000).
374 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado Informal waste pckng reduces the cost of a cty s sold waste management (SWM) program by reducng the amount of waste that needs to be collected, transported, and dsposed of, whch translates nto savngs to local governments and extends the lfe of dumps/landflls (Al et al., 1993; Baud and Schenk, 1994; Lardnos and Klundert, 1994; DGregoro, 1995; Assaad, 1996; Taylor, 1999; Medna, 2000; D Souza, 2001). Scavengng represents an ncome-generatng actvty for the poorest n the developng world. Medna (2000) estmates that, n Asan and Latn Amercan ctes, up to 2 per cent of the populaton survves by scavengng. Hogland and Marques (2000) report that 1 2 per cent of the populaton n large ctes n developng countres s supported by the refuse generated by the upper 10 20 per cent of the populaton. Unlke standard recyclng, waste-pckers recover materal from garbage that has already been dsposed of and put nto the muncpal sold waste stream. Wthout contrbuton of scavengng, ths valuable materal would be lost n landflls and dumpstes. Although SWM polces n both developed and developng countres seek to acheve the same envronmental goals, n practce ther mplementaton n the latter has been lmted due to lack of resources, partcular socoeconomc condtons, and severe dffcultes assocated wth enforceablty and montorng. Surprsngly, actvtes such as recyclng have shown hgh rates n developng countres compared wth more developed economes. Recyclng n developng countres, however, s not strctly the result of an envronmentally orented polcy. Informal waste-pckers n developng economes collect up to 40 per cent of the recyclable materal from the waste stream as a result of an ncome-generatng strategy. Ths actvty reflects both an effectve demand for recyclables by ndustry and low opportunty cost of labor from low-ncome and margnalzed groups that are able and wllng to engage n the actvty of recoverng recyclable materal from garbage. Despte ts sgnfcant contrbuton to the recovery and recyclng process, the role of nformal waste-pckers n muncpal waste management s stll not acknowledged (Ojeda-Benítez et al., 2002). Authortes n many developng countres do not fully realze the benefts of the recyclng carred out by scavengers, and ther actvty s ether banned or gnored when desgnng SWM polces and programs (Medna, 2000). Economc approaches for sold waste management SWM economc models are characterzed by the recognton of externaltes generated n the producton and dsposal of garbage, as well as the dentfcaton of economc nstruments to correct them. In the case of sold waste, the Pgouvan prescrpton establshes that a per-unt tax on the pollutng actvty, a waste-end tax that s equal to the margnal damage should be enough to nternalze effcently the externalty generated from waste dsposal. However, a waste-end tax s dffcult to mplement because waste s hard to montor and taxes are dffcult to enforce (Fullerton and Wolverton, 1999).
Envronment and Development Economcs 375 In order to deal wth these measurement and enforcement dffcultes, several authors have sought alternatve economc nstruments to deal effcently wth SWM. Some of the polces that have been proposed and evaluated nclude fees per unt of garbage (Callan and Thomas, 1999; Knnaman and Fullerton, 2002); advance dsposal fees, recyclng subsdes, and recyclng rate standards (Palmer et al., 1995; Walls and Palmer, 1997), among others. Other approaches nclude taxes on vrgn materal use or on producton processes as a means of reducng the generaton of sold wastes or ncreasng recyclng (Medema, 1983; Conrad, 1999). Two-part nstruments have also been proposed to address ncentve compatblty and adverse selecton problems assocated wth SWM. Ths knd of nstrument, usually the combnaton of a tax and a subsdy, has been studed for the case of waste dsposal usng dfferent approaches, the most wdely dscussed beng the depost-refund system, e.g. Macauley and Walls (2000). Holterman (1976) demonstrates that a tax on output and a subsdy on nputs can result n an effcent soluton when t s not possble to drectly tax an externalty. Confrmng Holterman s (1976) results, but opposng Conrad s (1999) and Medema s (1983) fndngs, Dnan (1993) shows that nstead of a vrgn materal tax, a combned dsposal tax and reuse subsdy s an effcent method of reducng waste. The dsposal tax provdes an effcent sgnal for source reducton and the reuse subsdy provdes an ncentve to use an effcent amount of recycled materals. A smlar approach has been suggested by Fullerton and Wolverton (1999), who generalze the depost refund system proposng a combnaton of a presumptve tax and an envronmental subsdy, whch do not need to be ether explctly lnked or equal to one another. They show that a twopart nstrument accomplshes the same effcency effect of a waste-end tax. The presumptve tax, a tax on the output, s mposed upon the assumpton ether that all producton uses a drty technology or that all consumpton goods become waste. Ths tax makes the good more expensve, reducng producton and therefore consumpton of the good, whch s analogous to the output effect of the waste-end tax. The envronmental subsdy s provded only f the producton uses clean technology or f consumpton goods are recycled. Ths subsdy makes waste more expensve relatve to other nputs of producton and reduces waste per unt of output, whch s analogous to the second effect of the waste-end tax, the substtuton effect. Another consderaton ncluded n SWM models s the effect of waste generaton on landfll depleton. Ready and Ready (1995), by treatng landfll as a depletable, replaceable asset, fnd that an optmal fee, whch ncreases as empty space reduces, mght be needed and, at low levels of depleton, s enough as a program for sold waste management. Our paper draws on the earler work of Moreno-Sánchez (1997), where she proposed a dynamc model of dsposal and recyclng for two recyclable goods n Bogotá, Colomba. We develop a dynamc model of producton, consumpton, dsposal, and recyclng, where the role of scavengers s explctly ntroduced. Empty landfll space s treated as a depletable resource and other natural resource stocks depleton s also ncluded to account for the mpact of usng vrgn materal compared wth recycled materal.
376 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado In several aspects, ths model could be seen as an extenson of the prevous models proposed by Fullerton and Wolverton (1999) and Dnan (1993), where two-part nstruments are used to deal wth sold waste dsposal externaltes. Our paper analyses SWM problems usng a more comprehensve approach that ntegrates prevous work and adjusts t to partcular condtons of sold waste systems n developng countres. Frst, the model ncludes the nter-temporal effects of landfll depleton; second, the externalty assocated wth the extracton of vrgn materal s ncluded as a falure dfferent from the externalty generated by the dsposal of the goods made from ths materal, and t s shown that those externaltes should be addressed usng dfferent and complementary nstruments. Fnally, the most mportant contrbuton of ths paper s the ncorporaton of waste-pckers nto the SWM systems n developng countres. The ncluson of waste-pckers n our model s grounded on fndngs by Baumol and Oates (1988), who show that, n the presence of shftable externaltes (postve externaltes from recyclng), t s effcent to target the economc nstrument (subsdy) to those agents who perceve the least margnal damage (the most margnal beneft) from the externalty; n ths case, waste-pckers. The model Several models have been proposed to analyze the behavor of economc agents facng the decson of waste generaton and recyclng. Suppose that from the many goods produced and consumed n a socety, there are n goods whose producton s based on natural resource extracton and these goods can be recycled. These goods, denoted by q p ( = 1,..., n), are produced usng ether extracted/harvested resources (X )ordomestc recycled materals 1 (R ). As n the standard case, labor (L ) and captal (K ) are ncluded n the producton functon. The producton functon can be wrtten as: q p = f (L, K, I ) where I = I (X, R ) = X + θ R = 1,..., n. (1) Here I s a functon that reflects how dfferent raw nputs (extracted resources, recycled materal) can be combned to produce good. Ths restrcton s assumed lnear whch mples that nputs are perfect substtutes. Includng ths relaton, the producton functon becomes q p = f (L, K, X, R ) = 1,..., n, (2) whch s assumed to exhbt decreasng margnal product for all the nputs. The lnear relatonshp among nputs can be manpulated to express X n terms of domestc recycled materal X = X (I, R ) = I θ R = 1,..., n. (3) Includng ths new relaton, the producton functon becomes q p = f (L, K, X(I, R ), R ) = f (L, K, R ) = 1,..., n. (4) 1 In ths paper, the terms recovered materal and recycled materal are ntended to have the same meanng. They refer to the materal collected by scavengers that s offered to the frms that produce fnal goods.
Envronment and Development Economcs 377 Ths relaton can be wrtten n terms of a transformaton functon ( p g q, L ), K, R 0 = 1,..., n. (5) Households consume the n goods, denoted by q c ( = 1,..., n), obtanng utlty. If we thnk of q c as packagng materals, they are converted nto waste when consumpton occurs. It mples that consumpton of q c generates utlty but, at the same tme, generates dsutlty to socety because of the garbage generated. Ths approach to ncorporatng the double effect of consumpton has been prevously suggested by Meyer (1971). Recycled materal comes from the waste produced domestcally. Consumed and dscarded goods can be ether dsposed of n the landfll (d ) or recycled n the producton process (R ), so that q c = d + R. Waste not recovered goes to the landfll. As depleton of empty landfll space s a dynamc process, we nclude tme consderatons to analyze t. The evoluton equaton for empty landfll space (B) s wrtten as follows Ḃ = d (t) = ( q c (t) R (t) ). (6) Recyclng these materals by waste-pckers requres labor (L R ) and captal (K R ) (waste pckng s consdered a labor-ntensve actvty). Waste-pckers do not dscrmnate among collected materal, so we have a mult-output transformaton functon g R (R 1,..., R n, L R, K R ) 0, (7) where R ( = 1,...,n) refers to the dfferent types of materals collected by waste-pckers. The other source of materal for producton s extracton (X ). Natural resources, renewable or non-renewable, used n the producton process are depleted over tme. If renewable, there exsts an ntrnsc growth functon h, whch may depend on the avalable stock S, and on envronmental condtons (E ). If the growth functon s denoted as h = h (S, E ), = 1,..., n, the evoluton equaton for the resource can be expressed as ds = Ṡ (t) = X (t) + h (S (t), E (t)). (8) dt For non-renewable resources h ( ) = 0. Suppose envronmental qualty matters to socety. Ths model consders two envronmental concerns. One s the depleton of empty space n the landfll. Currently, land space avalable for landflls s becomng ncreasngly scarce, manly n areas close to bg ctes, where they are most needed. As a result, socal welfare s affected by the depleton of empty space for waste dsposal. The second concern s the extracton and depleton of natural resources, whch mpact socal welfare. 2 The dstncton between these two types of externaltes s mportant n order to clarfy whch polcy 2 There s a concern drectly related to the actvty of waste-pckers tself, the negatve externaltes assocated wth use of publc space, road congeston, and the vsual mpacts they may cause to socety. These externaltes emerge only n the case of street waste-pckers. The net effect of these negatve and postve externaltes s an emprcal queston, and should be consdered on a case-by-case bass.
378 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado s best to solve each of the problems, a confuson that has emerged n some studes. These external effects are aggregated n a varable called envronmental qualty (A), whch s a functon of extracton and empty landfll space avalablty A = A(X 1,..., X n, B) = A(X, B), (9) where X s the vector of extracted resources {X 1,..., X n } and the functon has the propertes A X 0 (for = 1,..., n)anda B 0. Assume that a socal welfare functon (W) exsts. Ths functon depends on the amount of goods consumed (q c ), and on the envronmental qualty of the economy (A), W = W(q1 c,..., q n c, A(X, B)), and exhbts the usual convexty condtons. 3 Usng ths framework, the methodology we follow conssts of fndng, frst, the maxmzaton condtons of the socal welfare functon for ths economy and, then, the compettve equlbrum condtons for each group of agents. Comparson of these two sets of condtons allows us to dentfy market falures and to fnd optmal polces to solve them. Socal optmalty condtons The socal optmalty condtons are found by solvng the followng problem q c Max,R,q p T 0 ( W ( q c 1,..., q c n, A(X, B))) e ρt dt + F B (B(T))e ρt + n F (S (T))e ρt subject to the transformaton functons (equatons (5) and (7)), the evoluton equatons ((6) and (8)), market clearng condtons, ntal and termnal condtons for state varables, and non-negatvty condtons for control varables. Here, ρ refers to the dscount rate and F B (B(T)) and F (S (T)) are fnal value functons for stocks at termnal tme T. The objectve functon and evoluton equatons can be ntegrated nto a present value Hamltonan. Followng the maxmum prncple (Chang, 1992), a Lagrangan to nclude other restrctons s formulated and a current value Lagrangan s used to obtan the frst-order condtons. 4 The frst-order condtons wth respect to control varables (q c, q p ), assumng nteror solutons, are dw γ µ = 0 (10) dq c dg α dq p + µ = 0, (11) whch mply that the margnal utlty of consumpton of a unt of good must equal the margnal cost of producng t, plus the ntertemporal margnal =1 3 W q c 0, W q c q c 0, W x 0, W x x 0, W B 0, W BB 0. 4 Detals are avalable from the authors upon request.
Envronment and Development Economcs 379 cost of dsposng of ths unt n a landfll,.e., the margnal cost of reducng empty space n the landfll. The frst-order condtons wth respect to varable R mply that W A θ + γ + λ θ + α A X A X ( θ g X g R ) β g R R = 0 = 1,..., n, (12) W where θ A X s the margnal envronmental beneft to socety of recyclng one unt of nput and usng t n the producton of good, thus reducng the margnal damage caused by extracton; γ s the margnal beneft to socety of recyclng one unt of nput and avodng dsposal n a landfll; λ θ s the margnal nter-temporal beneft to socety of recyclng one unt of nput nstead of usng one unt of vrgn materal, thus avodng reducton of the stock of natural resources used n the producton g process; α (θ g R ) refers to the dfference between the margnal cost of producng good usng vrgn materal n terms of recycled materal and the margnal cost of producng good usng recycled materal. The sgn of ths expresson s ambguous: f postve, t reflects the margnal beneft of usng recycled materal nstead of vrgn materal n the producton process; f negatve, t represents the margnal cost of usng recycled materal nstead of vrgn materal n the producton process. The fnal term n equaton (12), β gr R, s the margnal cost of recoverng materal by waste-pckers. The condton wth respect to state varable B requres that the rate of change n the landfll space shadow prce should equal the sum of the margnal socal utlty of one unt of empty space and the proftablty of. keepng avalable a unt of empty space for next perod: γ = dw da da db + ργ. Also, the condton wth respect to state varable S shows that there should be equalty between the percentage rate of change n the shadow prce of every resource and the dfference between the dscount rate and the margnal growth of stock (whch s zero for non-renewable resources): λ λ = ρ dh ds for = 1,..., n. Other condtons from the maxmum prncple are those that recover the evoluton of stocks, the transformaton functons, the market clearng condtons, and the transversalty condtons. Compettve equlbrum condtons In ths economy, there are three groups of prvate agents: consumers, producers, and waste-pckers, each of them makng decsons ndependently. Ther market optmzaton condtons emerge from the followng problems: Consumers: Assumng a representatve consumer, or one of H dentcal consumers wth dentcal weght n the socal welfare functon, such an ndvdual wll seek to maxmze her utlty derved from consumng goods (q, = 1,..., n) and envronmental qualty (A), subject to a budget constrant. Ths ndvdual faces prces of goods p and an exogenous ncome m h. Dervng the maxmum prncple condtons related to control varables (qh c, = 1,..., n), the usual result s obtaned that the margnal utlty of the
380 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado last dollar spent on good should equal the margnal utlty of ncome for consumer h, and, therefore, be equal across all of the goods consumed by ndvdual h MUq h c = φ h = 1,..., n. (13) p Producers: Assumng a representatve producer of good, the problem for ths frm s to fnd the amount of nputs (recycled and vrgn materal, labor and captal) and of output (fnal product) that maxmze ts present value of benefts, subject to the technology and the evoluton equaton for extracton of vrgn materal. That s, the producer takes nto account the ntertemporal allocaton of the natural resource beng used for producton of good. Followng the maxmum prncple and the same procedure as followed n the socal optmalty condtons dervaton, the frst-order condtons are obtaned. For the control varables (q p, R ), these condtons are Lc g q p = p β q p = 0 = 1,..., n. (14) Ths equaton reflects the typcal margnal cost-prcng rule for producers actng compettvely. Lc = θ w x w R g g + θ λ + θ β β = 0 = 1,..., n, (15) R X R where θ w x s the margnal avoded cost (beneft) of usng one unt of domestc recycled materal nstead of vrgn materal n terms of recycled materal and w R s the margnal cost of usng domestc recycled materal. These two terms have meanng when nterpreted jontly. Wrtng (w R θ w x ), ths reflects the weghted (n terms of recycled nput) margnal ncremental cost (beneft) of usng recycled materal nstead of vrgn materal. θ λ s the nter-temporal margnal beneft of usng one unt of recycled materal, delayng the depleton of the natural resource used for producton of good. θ β g X β g R, reflects the ncremental value of the margnal product (beneft f greater than zero, or cost f less than zero) of usng recycled materal nstead of extracted materal n the producton process of good. Waste-pckers: Scavengers maxmze profts from collectng and sellng recycled materal subject to a transformaton functon. They face compettve prces n both output and factor markets, so they have to maxmze ther benefts subject to a labor-ntensve technology. Optmalty condtons for the control varable R mply the margnal cost-prcng rule for any producer under perfect competton p R β R dg R dr = 0 = 1,..., n. (16) Comparng the results In table 1, we can observe the smlartes and dfferences between the frst-order condtons from socal optmalty and those from compettve
Envronment and Development Economcs 381 Table 1. Comparson of frst-order condtons between socal optmalty and compettve equlbrum Varable Socal optmalty Compettve equlbrum q c = 1,..., n dw dq c γ µ = 0 (10) du h dq c φ h p = 0 (13) q p = 1,..., n R α dg dq p g + µ = 0 (11) p β q p = 0 (14) W A θ + γ + λ θ θ w x w R + θ λ A X ( g = 1,..., n + α θ g ) β g ( R g = 0 (12) + β θ g ) = 0 (15) X R R X R p R β R dg R dr = 0 (16) equlbrum. Comparng these two sets of condtons, the followng facts emerge. Consumpton of good (q c ): Assumng the socal welfare functon can be wrtten as a functon of all the ndvduals utltes, W = W(U 1,... U h,..., U m ), where U h = u h (qh c ; A), and comparng condtons (10) and (13) we obtan W U = 1 h φ, (17) h p = µ + γ. (18) Equaton (17) suggests that the weght for ndvdual h n the socal welfare functon should be the nverse of the margnal utlty of ncome for that ndvdual. Equaton (18) mples that n addton to the shadow prce of the good, the consumer prce must nclude the ntertemporal cost of usng up empty space that ths unt of consumpton wll create on the landfll s lfespan (γ ). Producton of good (q p ): From equatons (11) and (14) we have p = µ. (19) Equaton (19) says that the prce that producers receve should equal the shadow prce of the good. Producton of domestc recycled materal (R ): Addng equatons (15) and (16) and comparng wth equaton (12), we observe that n order for the market condtons to be an optmum, the followng must be true α = β, (20) β = β R, (21) p R = w R + γ, (22) w x = W A. (23) A X
382 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado The expressons n equatons (20) and (21) reflect the correspondence between the shadow prces from the socal optmalty and compettve equlbrum analyses. Equaton (22) mples that the prce that waste-pckers receve for domestc recycled materal should be the sum of the margnal producton cost and the margnal beneft to socety of savng an extra unt of empty space n the landfll through recyclng. Equaton (23) says that the prce of vrgn materal, w x, must nclude not only the extracton costs (whch n ths analyss are assumed to be zero) but also the cost of the negatve externalty caused to socety as a result of ths extracton. Polcy mplcatons For markets to be effcent, current condtons would requre that γ = 0and W A A X = 0. These terms are not zero, as externaltes exst n ths economy, therefore generatng market falures. In order for markets to reach a socal optmum, the followng set of polces should be ntroduced. Proposton 1: Consumers should pay a per-unt tax on consumpton equal to the margnal effect generated by the dsposal of the consumed unt n the landfll. Proof: Equatons (18) and (19) show that the prce producers receve should be dfferent from the prce consumers pay. The dfference s gven by the margnal damage generated by usng up empty space n the landfll. Therefore, consumers should pay not only the producer prce but also a per-unt tax equvalent to ths margnal damage. After a consumpton tax, t, consumers face a budget constrant wth a fnal prce on good equal to (p + t), as shown by Davs and Whnston (1962). Incorporatng ths new constrant n the utlty maxmzaton problem alters the frst-order condtons. Now, these condtons requre U h φ h (p + t ) = 0. (24) q c h Confrontng ths condton wth the socal optmalty condton (10), equaton (18) becomesp + t = µ + γ, and gven (19), then t = γ. Proposton 2: Waste-pckers should receve a per-unt subsdy on recovered materal gven by the margnal beneft generated to socety for avodng the use of empty space n the landfll. Proof: Equatons (18) and (19) mply that under compettve equlbrum, socety perceves γ to be zero. Ths undervaluaton of the mpact generated to socety due to the depleton of empty space n the landfll leads wastepckers to recover a sub-optmal amount of dscarded materal. A subsdy (s ) equal to the landfll empty space ntertemporal shadow prce (γ ) wll encourage waste-pckers to ncrease the domestc recycled materal up to the optmal level. Gven ths subsdy (s ), waste-pckers now face an output prce gven by (p R + s ) and then equaton (16) becomes ( ) p R g R + s βr = 0 = 1,..., n. (25) R Addng (25) and (15) and comparng wth (12) yeldsp R + s = w R + γ, and, gvenp R = w R, then s = γ.
Envronment and Development Economcs 383 Corollary: The per-unt consumpton tax s exactly equal to the per-unt recyclng subsdy, and equal to the ntertemporal margnal cost of reducng empty space n the landfll. Proposton 3: Producers of fnal goods that use natural resources as nputs should be charged a per-unt extracton tax equal to the margnal dsutlty generated to socety. Proof: From equaton (23) t s observed that, n order to reach optmalty, producers usng vrgn materal should assume not only the extracton costs but also the cost of the negatve externalty generated to socety from ths extracton. It s worth notcng that ths externalty does not refer to the ntertemporal allocaton of the resource beng exploted. The ntertemporal effect s already accounted for through the shadow prce (λ ). Producers payng a per-unt extracton tax (z ) now face a prce on extracted resources equal to (w x + z ), and thus condton (15) becomes ( ) w x + z θ w R g + θ λ + β (θ g ) = 0. (26) X R Addng condtons (26) and (16) and comparng wth condton (12) mples that equaton (23) becomes w x + z = W A A dx. If w x accounts for the extracton and processng cost, then z = W A A dx. Dscusson The model proposed here ncludes two market falures assocated wth sold waste systems. One of them refers to the lack of nternalzaton of the nter-temporal costs assocated wth the depleton of the empty space n the landfll. The other one concerns the envronmental costs assocated wth extracton of vrgn materal for the producton of goods that, n the end, need to be dsposed of. Ths dscrmnaton s mportant because, n some studes, the envronmental cost assocated wth extracton of vrgn materal s gnored and, nstead, a tax on vrgn materal s proposed n order to encourage effcent dsposal of sold waste. For nstance, Medema (1983) advocates the use of vrgn materal fees as a means of motvatng effcent waste dsposal practces,.e. encouragng recyclng and reducng the dsposal of sold waste. Although vrgn materal fees can, n fact, ncrease the demand for recycled materals and hence reduce dsposal requrements, Dnan (1993) shows that there are mportant drawbacks n terms of effcency assocated wth usng vrgn materal fees to reduce dsposal requrements. He demonstrates that a vrgn materal tax cannot result n an optmal resource allocaton but that a combned dsposal tax and reuse subsdy polcy can. In our model, we show that a tax on vrgn materal extracton s needed, not to deal wth the externalty assocated wth waste dsposal but to nternalze the externalty assocated wth envronmental damage from extracton of vrgn materal. Dfferentatng these effects leads one to recognze the need for dfferent polces amed at correctng each of these falures. The externalty assocated wth waste dsposal, as Fullerton and Wolverton (1999) demonstrate, should be addressed through a two-part
384 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado nstrument: a presumptve tax and an envronmental subsdy. Thus, our model proposes three smultaneous polces. A tax on vrgn-materal extracton, not amed at the fnal purpose of reducng dsposal of sold waste, but nstead targeted at the externalty assocated wth raw materal extracton. The other two polces act as a two-part nstrument, whch n our case corresponds to a dsposal tax and a reuse/recyclng subsdy. Compared wth a Pgouvan tax, e.g. unt-based prcng or waste-end tax, the combnaton of a tax on consumers and subsdy to recyclng has the same practcal advantages as the two-part nstrument proposed by Fullerton and Wolverton (1999). Partcularly, the two-part nstrument s easer to enforce and dscourages llegal dsposal. On the other hand, under unt-based prcng, households would be charged the same for each unt of trash, regardless of the contents. Not all types of trash mpose the same dsposal costs, however. As Dnan (1993) states, a tax-reuse subsdy polcy may be better suted to deal wth potentally recyclable waste tems that have hgher than average dsposal costs. Admnstratvely, Fullerton and Wolverton (1999) argue that a two-part nstrument wll often have lower costs than a waste-end tax. However, Dnan (1993) argues that admnstraton of ths nstrument can be very expensve f all the tems from the waste stream are ncluded. Ths polcy would be best targeted at selected tems n the waste stream: for nstance, those tems that have a hgher share n the composton of waste or those that have hgher envronmental mpact. In our model, the externalty generated on empty landfll space depleton can be measured n terms of the volume that the tem occupes n the landfll. So, those tems wth hgher volume and hgher share n the waste stream are best canddates for the mplementaton of ths polcy. In addton, the two-part nstrument has the advantage that t s selffnancng. The subsdy can be taken drectly from the tax collected on consumers. Although Fullerton and Wolverton (1999) demonstrate that, under some condtons, the tax and the subsdy can dffer, n our model they concde snce both of them are drectly related to the margnal ntertemporal value of empty space n the landfll (γ ). The margnal damage that generates one unt of garbage dsposed of by a consumer s exactly the same margnal beneft that generates ths unt collected and recycled by waste-pckers. Fnally, wth respect to the prcng of the nstruments, smlar to the case of a Pgouvan tax, the rate of the dsposal tax and the recyclng subsdy wll need to be adjusted by tral and error because authortes cannot know aprorthe exact amounts to nduce optmal behavor of nvolved agents. We argue that, for developng countres, the envronmental subsdy should be amed at favorng scavengers actvty. As Fullerton and Wolverton (1999) state, f markets work, the subsdy can be passed on to supplers of recycled goods. Specfcally, these authors assert that one of the attrbutes of the depost refund system s that the depost does not need to be clamed by the orgnal purchaser, n our case, the consumer who pays the tax. The ncentve to collect and return the tem s effectvely transferred to the agents wth the lowest opportunty cost of tme. Ths s n accordance wth Baumol and Oates (1988) fndngs, whch show the effcency of transferrng the externalty to the group wth the least margnal
Envronment and Development Economcs 385 damage (the most margnal beneft). For nstance, householders wth hgh tme value mght not fnd t worthwhle to separate and recycle beverage bottles, snce the margnal beneft assocated wth ths actvty s too low compared wth ts margnal cost. Conversely, waste-pckers can recover the materal and capture ts value, obtanng a hgh margnal beneft due to ther need for ncome and the low opportunty cost of ther tme. In turn, the subsdy wll beneft more waste-pckers who have a hgher margnal utlty of ncome than householders. So, ths polcy not only would lead to an effcent outcome,.e. maxmzng socal welfare, but also would mply mportant dstrbutonal effects. The subsdy proposed here to scavengers mght become admnstratvely expensve because of the large number of people devoted to ths actvty and ts hghly nformal nature. A way of reducng these admnstratve costs s to target the subsdy to organzed scavengers groups. Thus, a frst step requres organzatonal and techncal support to scavengng actvty through the formaton of cooperatve socetes or mcro-enterprses. In some Latn Amercan countres such as Brazl, Colomba, Mexco, Peru, and some Asan countres such as Indonesa and Malaysa, scavengers have acheved dfferent levels of organzaton, whch has allowed them to be ncluded as an mportant actor n formal SWM systems. Funds from the receved subsdy mght be orented to: () mprovng workng condtons and facltes, () achevng more favorable marketng arrangements for servces and scavenged materals, and () ntroducng health protecton and socal securty measures. Numercal smulaton Gven the nformalty assocated wth the collecton and recyclng of sold waste by waste-pckers, relable data are extremely scarce and when avalable they are lmted to case studes wth aggregated nformaton. Therefore, econometrc analyss cannot be performed n order to obtan ether producton functons for scavengng actvty or margnal beneft (damage) functons from generaton and dsposal of sold waste. Thus, optmal values for economc nstruments cannot be derved from actual nformaton. In order to get a sense of the mplcatons of the proposed set of polces on the most relevant varables analyzed n the theoretcal model, we perform a numercal smulaton. 5 For smplcty, a unque good s assumed to be produced, consumed, and able to be recycled. The smulaton s focused on the varables of nterest,.e. empty landfll space, resource stock and extracton, waste recovery, and envronmental qualty. The frst step s to assume functonal forms for the socal welfare functon and producton functons to be ncorporated nto the theoretcal model. The socal welfare functon s assumed to be Cobb Douglas. The producton functon for the good s also assumed to be Cobb Douglas wth decreasng returns to scale and perfect substtutablty between extracted and recycled nput. Producers are n charge of extracton, so they face an extracton 5 Full detals about used data, calbraton and smulaton are avalable from the authors upon request.
386 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado Table 2. Specfcaton of the equatons and the parameter values assumed n the numercal smulaton Parameter Value Interpretaton Utlty functon: W = W(q, A(X, B)) = Dq γ A 1 γ, A(X, B) = ln(b) ln(x + 1) γ 0.6 Parameter for consumpton n Cobb Douglas utlty functon D 10 Utlty functon parameter Producton functon: q = q(x, R) = M(X + R) β Extracton cost functon: C = C(X, S) = cx 2 /2S β 0.306 Parameter for nputs n Cobb Douglas producton functon M 2,673 Producton functon techncal parameter c 11,333 Parameter n extracton cost functon Waste-pckers producton functon: R = R(L, K ) = θ L α 1 K α 2 α 1 0.49 Parameter for labor n Cobb Douglas recovery functon α 2 0.26 Parameter for captal n Cobb Douglas recovery functon θ 21.82 Recovery functon techncal parameter Intal values for stock varables Varable Intal value Unts Empty landfll space (B) 3 10 7 Tons Natural resource (S) 1 10 7 Tons Market Prces Varable Value Unts Commodty 80 US $/ton Recovered materal 34 US $/ton Scavengers labor 25 US $/man/month Scavengers captal 20 US $/equpment unt/month cost functon wth the standard assumpton of ncreasng costs as the stock reduces. The producton functon for waste-pckers s assumed to have a Cobb Douglas functonal form, be labor ntensve, and have decreasng returns to scale. Usng these functons, the model s solved analytcally and expressons for the optmal polcy nstruments (consumpton tax, recyclng subsdy, and extracton tax) obtaned. The numercal smulaton s based on data from Bogotá (Colomba). Unknown parameters were obtaned through numercal approxmaton from known data. Specfcaton of the equatons and the parameter values assumed n the smulatons are presented n table 2.
Envronment and Development Economcs 387 Table 3. Results from the numercal smulaton. Percentage changes n man varables durng the 20-year perod of analyss compared to the baselne under three scenaros: optmal-level nstruments, low-level nstruments and hgh-level nstruments Optmal-level nstruments Low-level nstruments Hgh-level nstruments Varable Frst Year Last year Frst year Last year Frst year Last year Empty space 0 40 0 18 0 62 avalablty Resource stock 0 18 0 8 0 27 avalablty Resource extracton 23 9 12 4 33 15 Recyclng 95 42 42 20 146 70 Envronmental qualty 4 6 2 3 6 9.5 Consumpton of the 8 7 4 3 12 9 good Utlty 3.5 1.4 2 0.8 5 2 The model s frst calbrated for the baselne case, and then smulated under the optmal polces to observe the mpact on the varables of nterest over a 20-year perod. The man results are presented n table 3 (column 2). From the smulaton t s observed that the set of optmal polces ncreases the avalablty of empty space of the landfll by about 40 per cent at the end of the 20-year perod. Ths s the result of both a reducton n consumpton of the good (output effect) and an ncrease n the amount of recycled materal (substtuton effect). The natural resource stock s extracted at a lower pace as a result of the set of polces. After 20 years, there are savngs correspondng to 18 per cent of the orgnal stock. Consequently, extracton s reduced durng all the perods of analyss. Recovery and recyclng of sold waste (R) s encouraged when optmal polces are mplemented, and t ncreases by nearly 95 per cent at the begnnng and reduces to 42 per cent by the end of the 20-year perod, showng that recovery and recyclng performed by waste pckers turns out to be the most elastc varable to changes n prces as a result of the set of polces. The combnaton of reduced prces of recycled materal for fnal good producers and greater prces of extracted materal pushes the use of recovered materal up. Envronmental qualty exhbts an nterestng path: wth no polcy n place, the envronmental qualty functon reaches a maxmum after 13 years, and then decreases rapdly as a consequence of the reducton n empty space. When the optmal polces are ncluded, envronmental qualty takes greater values for every perod, and even after 20 years the maxmum s stll not reached. Ths s a result of both the reducton n the extracton of natural resource,.e. the externaltes assocated wth t, and an ncrease n the avalable empty space n the landfll. On average, envronmental qualty ncreases by 5 per cent as a result of the polcy durng the 20-year perod.
388 Rocío Del Plar Moreno-Sánchez and Jorge Hgno Maldonado The results from the numercal smulaton confrm the results obtaned from the theoretcal model. These results, however, are specfc to the assumptons and data adopted and further applcatons should be analyzed for partcular cases. To gve some flexblty to the results, a senstvty analyss s also performed. Two addtonal scenaros are proposed for comparson: a low-level tax polcy and a hgh-level tax polcy (see table 3, columns 3 and 4). In the low-level tax scenaro, the two taxes and the subsdy are reduced to a half of the calculated optmal values for each year n the smulaton perod. In the hgh-level tax scenaro, the value of each of the nstruments s ncreased by 50 per cent compared wth every-year calculated optmal value. The hgh-level tax polcy ncreases the savngs n empty space up to 62 per cent after the 20 years of analyss, whle ncreasng the savngs n natural resource stock up to more than 25 per cent. Ths mples a reducton n the use of the extracted resource of more than 30 per cent durng the frst years. Recyclng, beng the most senstve actvty to the polcy, s ncreased up to a maxmum of nearly 150 per cent compared wth the baselne. As a result of these changes, envronmental qualty ncreases are n the range of 6 to 9 per cent as a result of the hgh-level tax polcy. Even though consumpton s reduced n the frst years up to 12 per cent, utlty s only reduced up to a maxmum of 5 per cent. Ths s explaned by the fact that reducton n consumpton s offset by the ncrease n envronmental qualty. For the case of the low-level tax, polcy changes are smoother compared to the optmal case. The most sgnfcant change s recyclng, whch ncreases more than 40 per cent durng the frst years, compared wth the baselne. Gven the hghly non-lnear nature of the equatons, and of the system as a whole, the stablty of the results from the senstvty analyss around the optmal polces demonstrates that there s some range of values where polces can be put n place and expected results can be obtaned. Ths mples that polcymakers do not need to have perfect knowledge of the exact optmum values to start mplementng a polcy and that some tral and error n applcaton s possble n practce. Conclusons Scavengng s a growng phenomenon n large ctes of the developng world. Ths actvty s not only a source of ncome for many people facng precarous economc condtons, but t also generates a postve envronmental externalty on natural resource use and on landfll lfespan. Informal waste-pckng actvtes should be encouraged and successful experences should be replcated. Wth the ncreasng trend towards prvatzaton of servces and the drve for ncreased effcency, legslatve frameworks and contracts should be flexble enough to allow the partcpaton of small-scale servce provders, e.g. groups of organzed waste-pckers. The Pgouvan prescrpton mples that such a postve externalty should be encouraged wth a subsdy equal to the margnal beneft to socety. Ths model shows that n a dynamc framework the prescrpton s stll vald, though correctons over tme should be ncluded. The model generates a polcy prescrpton that s dynamc n nature. Although optmal, changng the values of the tax every perod would mply prohbtve polces due to
Envronment and Development Economcs 389 hgh transacton and admnstratve costs and they would be mpractcal. Instead, what the model suggests s the defnton of a set of taxes that consder ntertemporal relatonshps but that can be set at a certan level and be revsed perodcally dependng on the evoluton of condtons n the economy. The optmal set of polces from ths model comprses a combnaton of polces smlar to the two-part nstrument proposed by Fullerton and Wolverton (1999): a tax on households per unt of good consumed equal to the shadow prce of the empty landfll space, and a subsdy to wastepckers per unt of materal recovered and saved from beng dsposed n the landfll, equal to the shadow prce of empty landfll space. In addton to these two nstruments, a tax on frms extractng vrgn resources equal to the margnal damage generated by extracton of the resource s also needed to reach effcency n ths economy. The optmal subsdy to waste-pckers under perfect competton must equal the tax on consumers, whch mples a transfer from consumers to waste-pckers. The optmal tax and subsdy should be determned based on the equvalent space that each commodty would use n the landfll. Gven that consumpton of packagng goods s drectly related to ncome, the tax would not be regressve, f equty consderatons are to be ncluded. Besdes, drectng the subsdy towards waste-pckers not only leads to the effcency of the polcy but also accounts for dstrbutonal effects that help the least favored groups n developng country economes. Industres that consume recyclables n developng countres encourage and support the exstence of waste dealers between them and waste-pckers n order to assure an adequate volume and qualty of the materals. As a result, opportuntes arse for exercsng market power. Several authors suggest that the low prces that waste-pckers receve are due to the presence of mperfect competton n the market for recovered materal (Kaseva and Gupta, 1996; Medna, 2000; Ojeda-Benítez et al., 2002). An extenson to ths model would be the ncorporaton of mperfect competton n waste collecton. Impacts from trade mght also be consdered. Some developed countres are able to produce recycled materal of a hgher qualty compared wth recycled materal n developng countres. Gven envronmental regulaton n developed countres, frms may be nterested n dvertng recyclng surpluses to developng countres. Although these mports may reduce producton costs n developng countres, they generate two negatve mpacts. Frst, domestc recyclng by waste-pckers n developng countres mght be dscouraged, wth the socal mplcatons of unemployment and ndgence for these people on the socal frnge. Second, domestc landflls would be exposed to hgher pressure because they would have to receve domestc waste not recovered, n addton to the garbage comng from the mported materal. Ths would be a case of losses from trade that should be carefully consdered to avod addtonal dstortons that can be costly economcally and socally. Further research n ths area s encouraged. The mplcatons of ths paper do not mean that msery condtons of waste-pckers n developng countres should be encouraged. Rather, they