Economic incentives and the quality of domestic waste: counterproductive effects through waste leakage 1

Transcription

1 Economc ncentves and the qualty of domestc waste: counterproductve effects through waste leakage 1 H. Bartelngs 2, R. B. Dellnk and E.C. van Ierland, Envronmental Economcs and Natural Resources Group, Wagenngen Unversty P.O. Box 8130, 6700 EW Wagenngen, The Netherlands Abstract In ths paper, we show that ntroducng a unt based fee for the collecton of household waste may lead to undesrable envronmental mpacts. Such a fee provdes households ncentves to generate lower qualty organc waste as a form of dumpng. An appled general equlbrum model s bult that ncorporates organc waste n hgh qualty, low qualty, and rest waste, ncludng the possblty of substtuton between the generaton of these three types of waste. The model s used to analyze the effects of ntroducng a unt-based prcng scheme. The results show that waste leakage can occur and that ths wll have a strong mpact on the effectveness of the unt-based prcng scheme. The successfulness of unt-based prcng largely depends on the wllngness of the households. Households wth a large preference for a clean envronment are less lkely to dump rest waste n organc waste. Ths makes untbased prcng less sutable for larger muncpaltes, whch n general have a larger share of ordnary consumers who have only small preference for a clean envronment. We recommend consderng these counterproductve effects explctly before mplementng unt-based prcng of waste collecton. 1

2 Keywords: Flat fee; General equlbrum; Polcy modelng; Sold waste; Unt-based prcng; JEL classfcaton: D58; H21; Q28 1 Introducton Economc lterature suggests that externaltes should be nternalzed by means of Pgovan taxaton. To nternalze the external costs of waste dumpng a unt-based prcng scheme 3 for the collecton of sold waste can be mplemented. Most muncpaltes, however, stll favor the flat fee-prcng scheme 4 over the varableprcng scheme. Recent studes have shown that the ntroducton of such a Pgovan tax contrbutes to solvng the sold waste problem, provded that proper care s taken to prevent llegal dsposal, lke dumpng and llegal burnng (see for example Jenkns, 1993; Fullerton and Knnaman, 1995, 1996; Palmer and Walls, 1997; Fullerton and Wu, 1998 and Choe and Fraser, 1999). Dsposal taxes also gve ncentves to producers to make effcent choces about the degree of packagng, the weght and materal nput of the product and fnally the rate of recyclablty of the product (Fullerton and Wu, 1998). Several muncpaltes have already expermented wth the use of varable taxes for waste collecton. Results of these experments can be found n, for example, Mranda et al. (1994), Sterner and Bartelngs (1999), and Lnderhof et al. (2001). Most of these emprcal studes conclude n favor of the Pgovan tax. 2

3 A unt-based prcng scheme s usually only mplemented for collecton of rest waste. Households can choose to separate organc waste and paper, whch s collected free of charge. A unt-based prcng system s generally accompaned wth polces promotng recyclng of glass, tns, and batteres. Recent studes (see for example Fullerton and Knnaman, 1995) have focused on the possblty of llegal dsposal of waste as a consequence of ntroducng untbased prcng system for waste collecton. However, they have faled to recognze another potental problem, namely the possblty of polluton of recyclable or organc waste. Not only do households have the opton of burnng or llegally dumpng trash but they also can get rd of the rest waste n small amounts by puttng t n wth organc waste or glass contaners--both of whch are collected free of charge. Ths knd of waste leakage can have serous effects. It wll greatly ncrease the costs of recyclng or compostng of polluted waste. Ths could eventually, result n the stuaton where all waste s ncnerated or landflled. Especally n larger muncpaltes ths could be a sgnfcant problem. Montorng and preventng waste leakage s costly. Organc waste s usually collected n large garbage trucks where all waste s thrown together. Ths makes t dffcult to dstngush waste of one household from that of another. To locate the source of polluted organc waste, the qualty of organc waste must be checked durng collecton. Ths requres large adaptaton costs and t would probably be cheaper to separate the organc waste from the rest waste at the compostng unt. Although ths paper focuses on waste leakage n a unt-based prcng system, waste leakage s a potental problem n any system n whch consumers are punshed for generatng rest waste and rewarded for generatng recyclable or organc waste. 3

4 In ths paper we apply a general equlbrum approach to buld a model wth whch the problem of waste leakage can be analyzed. Exstng studes have analyzed economc and envronmental effects of polces amed at reducng waste generaton, n both partal equlbrum and general equlbrum. Most recent studes have chosen the general equlbrum approach. The advantage of a general equlbrum approach over a partal equlbrum approach s, frstly, that t s possble to model the entre product lfe-cycle from producton, packagng, sale, use to dsposal. Polces tryng to reduce waste dsposal wll effect all of these stages n the lfe-cycle. It s, therefore, essental to nclude all these stages n the model. Secondly, waste leakage s a sort of market falure. Ths market falure wll not only affect the compostng market but all other markets n the model. To gnore these effects wll gve an ncomplete pcture of the mpacts waste leakage has on our economy. We wll show wth a numercal example, based on data stylzed for the Netherlands n 1996, that waste leakage can cause serous problems. Consumers wll have an ncentve to pollute organc waste, whch n turn wll greatly ncrease the cost of compostng and recyclng. Envronmental preferences of a household play an mportant role n decdng what qualty of organc waste the household wants to generate. Households wth lttle or no preference for a clean envronment wll have a larger ncentve to pollute organc waste than those households wth a larger preference for a clean envronment. Ths aspect wll be mplemented n the model by ntroducng two groups of consumers: green consumers and ordnary consumers, who face dfferent substtuton elastctes between organc waste and rest waste. The paper s structured as follows. Secton 2 descrbes the model and shows how the problem of waste leakage can be ncluded n an appled general equlbrum 4

5 model. Secton 3 presents a numercal example and shows how a unt-based prcng system can nadvertently promote waste leakage. Secton 4 concludes and gves polcy recommendatons. 2 Modelng dfferent waste categores 2.1 Model descrpton The model used n ths paper s an appled general equlbrum model (AGE) n the Negsh format 5. In ths secton a general model descrpton s gven. The focus s on the assumptons necessary to buld a model that ncludes generaton of three types of waste, a flat fee prcng system and a varable labor supply 6. To llustrate the problem of waste leakage clearly, the model has been kept as smple as possble. Ths makes t easy to follow the assumptons necessary to ntroduce waste leakage n an AGE model. The model characterstcs are as follows. There are three consumers n the model: two prvate households and a government. Prvate households generate waste as a fxed percentage of consumpton and they have to deal wth ths waste. They can ether choose to put the waste n the waste bn or chose to separate organc waste from rest waste. The organc waste s then collected separately from the rest waste and sent to a compostng unt (see fgure 1). {enter fgure 1 here} Generatng organc waste s costly for the consumers because they have to nvest labor to separate organc waste from rest waste. The consumers can choose to 5

6 generate low or hgh qualty organc waste. Producton of a hgh qualty organc waste wll cost more labor. In the benchmark model, prvate households pay a flat fee for collecton of all waste, ncludng organc and rest waste 7. In such a prcng scheme, the margnal costs of waste collecton equal zero. Ths means that the equlbrum prce for waste collecton of rest waste and organc waste equals zero. To mplement ths n the Negsh format, a subsdy-cum-tax scheme s used. In the subsdy-cum-tax scheme, consumers pay the equlbrum prce for waste collecton. However, the government remburses the consumers wth exactly the same amount n the form of a subsdy. In ths case the perceved prce for addtonal waste dsposal equals zero. The government wll fnance the costs of the subsdy by demandng a flat fee or drect tax 8 from the prvate households for waste collecton. In the polcy change scenaro a unt-based prcng scheme s ntroduced for the collecton of rest waste. Ths means that prvate households pay the equlbrum prce for waste collecton, whch equals the margnal costs of producng these servces. 2.2 The model Our smple model follows the general structure of an AGE model n the Negsh format. Therefore, total welfare s maxmzed. Total welfare (TW) depends on the weghted sum of the log of the utltes, u, of each consumer where =1..3, wth welfare weghts, α, (see appendx A and B for full model specfcaton and notaton) 9 : TW = α ln( u ) (2.1) Prvate households generate waste durng consumpton. For smplcty, we have chosen to keep our model statc, although we realze that waste generaton has 6

7 dynamc aspects; not all products wll turn nto waste mmedately when they are consumed, for example durables can functon properly for several years. In our comparatve statc model, waste generaton (W) of consumer s determned as a fracton β of the consumpton product, x g 10. W = β x g (2.2) The prvate households have to deal wth the waste by usng the so-called waste collecton servces. They can ether choose to demand collecton servces of rest waste, x r, or collecton servces of organc waste, x o. They can substtute between demand of rest waste collecton servces and organc waste collecton servces. Prvate households can also choose to generate low qualty organc waste, x o,l, or hgh qualty organc waste, x o,h, as specfed n the followng CES functon 11 : W CES x CES x x σ σ r o, l o, h l h ro = (, (, ; ); ) (2.3) Where σ lh stands for the substtuton elastcty between low qualty organc waste and hgh qualty organc waste and σ ro stands for the substtuton elastcty between rest waste and organc waste. The demand for collecton servces s not equal to the generaton of waste. To convert from demand for a certan type of collecton servce (n volume) to the actual generaton of that type of waste (n kg) we calculate that partcular collecton servce s share of total collecton servce demand. We then multply ths by the total amount of waste generated, calculated as a percentage of consumpton. If the prvate households decde to generate organc waste, they wll spend labor, lw, on separatng organc waste from rest waste. Producng hgh qualty organc waste costs more labor than producng low qualty organc waste. The producton possblty set for organc waste of qualty f looks as follows, (f=1,2): 7

8 x µ lw o, f f f (2.4) Where µ reflects the labor costs necessary to produce a unt of organc waste of qualty f. The three frms (producers of the consumpton goods and the two types of collecton servces) generate output q of good j under condtons of constant returns to scale, usng as nputs captal, k, and labor, l. Thus the producton functon for these frms s: j j j j q = CES( k, l ; σ kl ) (2.5) Where σ kl s the substtuton elastcty between captal and labor. Consumers supply captal and labor to the frms. The captal supply, K, s exogenously determned. However, the labor supply L of each consumer s calculated as the exogenous labor endowment, L, mnus the total amount of labor used for generatng both types of organc waste, lw f : L L lw f = (2.6) f The model s closed by two balance constrants: () the commodty balance constrant, whch states that demand for any commodty should be less than or equal to the supply of that commodty 12, 13 : g r c j p k x + TW + TW q + K + L (2.7) j and () the subsdy balance constrants for both types of collecton servces: x TW p r r r t f x TW p o, f o c t (2.8) (2.9) 8

9 By takng the margnal value of the subsdy balance constrants, equaton (2.8) and (2.9), the perceved prce of both waste collecton servces can be determned. In the case of the flat fee prcng scheme ths prce wll equal zero. Fnally, the Negsh weghts are determned n such a way that each of the consumers spends ther full ncome on the consumpton of goods and servces. 3 A numercal example The model presented above s appled n a numercal example wth stylzed data from the Netherlands. The goal of ths secton s to show how the man mechansms of the model operate and how these mechansms are nfluenced by the assumptons nherent n the model. The economc data used n the numercal example are based on the Netherlands n 1996 (Statstcs Netherlands, 1998). 3.1 Benchmark data The accountng matrx dsplayed n Table I descrbes the ntal equlbrum. Supply of commodtes,.e. producers output and consumer endowments, have postve values; demand of commodtes,.e. producton nputs and consumpton, have negatve values 14. {enter table I here} 9

10 In the benchmark scenaro prvate households pay a flat fee for the collecton of both rest waste and organc waste. Ths fee covers about 95% of the actual cost of waste collecton. Although the fee (and the cost-coverage rate) vares a lot between dfferent muncpaltes n the Netherlands, the average cost-coverage rate of all the muncpaltes s around 95%. All prces are normalzed to unty except the prces for waste collecton of rest waste and organc waste. For these collecton servces two prces can be dstngushed: the prvate prce of waste collecton and the socal prce of waste collecton. Consumers pay a prce for waste collecton, whch equals the total fee dvded by the total demand for waste collecton. The socal prce for waste collecton s equal to the total fee plus the total amount pad by the government for waste collecton, all dvded by the total demand for waste collecton. We have chosen to normalze the prvate prce for waste collecton, whch means that the socal prce for waste collecton (as shown n Table I) s hgher than unty. Prvate households can generate three categores of waste. Rest waste can be generated wthout costs, where as generaton of both types of organc waste requres labor. A hgher qualty of organc waste requres more labor nput than a lower qualty. Addtonal data about the generaton of organc waste s gven n Table II. {enter table II here) The prvate households are dvded nto two groups, the so-called tradtonal households (Cons1) and the green households (Cons2). The tradtonal households do not have a specfc preference to preserve the envronment, but the green households do. These dfferences n envronmental preferences are captured n the 10

11 substtuton elastctes between rest waste and organc waste and between hgh and low qualty organc waste. The actual substtuton elastctes used n the model are shown n Table III. {enter table III here} 3.2 Results The model as specfed above s used to calculate the effects of ntroducng a untbased prcng scheme for the collecton of rest waste. Ths means that prvate households wll have to pay the equlbrum prce (whch equals the margnal costs of producng ths servce) for the collecton of rest waste. Prvate households wll stll pay a flat fee for the collecton of organc waste. Comparng the benchmark stuaton, wth the flat fee prcng scheme, to the scenaro wth the unt-based prcng scheme wll gve an ndcaton of the expected results of ntroducng such a polcy change. In Table IV the changes n the man varables are shown. {enter table IV here} As shown n Table IV, ntroducng a unt based prcng scheme for collecton of rest waste has a dramatc effect on the demand for collecton of rest waste and the demand for collecton of organc waste. These results are as expected, snce organc waste can be collected free of charge, households wll start to substtute the more expensve rest waste wth organc waste. Ths holds especally for the ordnary consumer who has a 11

12 hgh substtuton elastcty between rest waste and organc waste. The polcy, however, also has the undesrable effect that the quantty of low qualty organc waste s ncreased (Table V). {enter table V here} Prvate households start to produce far more low qualty organc waste nstead of hgh qualty organc waste (see Table V). Substtuton of rest waste producton for low qualty organc waste s especally evdent among tradtonal consumers. Green consumers, who have more concern for the envronment, ncrease both ther producton of low qualty organc waste and ther producton of hgh qualty organc waste. Snce both types of organc waste are collected together, the share of low qualty organc waste wll greatly affect the overall qualty. If the amount of low qualty organc waste s relatvely large compared to the amount of hgh qualty organc waste then the overall qualty of the organc waste wll be low. Ths can result n ether hgh costs for compostng. snce the organc waste has to be sorted frst, or n a stuaton where the organc waste cannot be composted. Waste n the latter category must ether be ncnerated or landflled. Table V shows that the share of low qualty organc waste has greatly ncreased. The unt-based prcng scheme causes waste leakage and s therefore not sutable to provde ncentves to prvate households to mnmze waste producton. 3.3 Senstvty analyss 12

13 Ths secton deals wth the senstvty of the model. The results as presented n the prevous secton depend largely on the exogenous parameters used. Especally four parameters that are dffcult to measure or estmate need careful examnaton. These four parameters are: () the substtuton elastcty between rest waste and organc waste; () the substtuton elastcty between low qualty organc waste and hgh qualty organc waste; () the labor cost of generatng low and hgh qualty organc waste, and (v) the ncome share of the green consumer n the total ncome. The followng procedure s used for the senstvty analyss. For each of the parameters a reasonable lower and upper bound s determned. Then the value of the parameter s changed n a number of (equdstant) steps from the lower to the upper value. The effects of parameter changes on the varables: rest waste, low qualty organc waste and hgh qualty organc waste are then calculated Substtuton elastcty between rest waste and organc waste The frst parameter to be analyzed s the substtuton elastcty between rest waste and organc waste. Ths substtuton elastcty s lower for the green consumer than the tradtonal consumer. We have chosen to keep the rato of the substtuton elastctes between both consumers constant. Fgure 2 shows the results of the senstvty analyss. All other parameters are kept constant at benchmark levels. The substtuton elastcty between rest waste and organc waste determnes how much rest waste s generated. If the substtuton elastcty s qute hgh then only 2.5 mllon tonnes of rest waste s generated. If, however. the elastcty s qute low the amount of rest waste s almost trpled. Note that the amount of low qualty organc waste ncreases sharply, so most of the rest waste that s avoded has been turned nto 13

14 low qualty organc waste. The amount of hgh qualty organc waste generated also ncreases, but far slower than the quantty of low qualty organc waste. {enter fgure 2 here} Substtuton elastcty between low qualty and hgh qualty organc waste The second parameter that s changed s the substtuton elastcty between low qualty and hgh qualty organc waste. Ths substtuton elastcty dffers between the two consumers and the rato between these two elastctes has been kept constant. The results of ths senstvty analyss are shown n Fgure 3. {enter fgure 3 here} The amount of low qualty compost generated s very senstve to ths substtuton elastcty. If the substtuton elastcty s low, a relatvely large quantty of hgh qualty organc waste s generated. The amount of rest waste generated s also qute hgh. Ths s as expected because a low substtuton elastcty mples an nelastc demand for collecton of hgh qualty organc waste. If the elastcty s hgh, both consumers have an elastc demand for collecton of hgh qualty organc waste, then most of the waste s transformed n cheaper low qualty organc waste. Only a relatvely small percentage s transformed nto the categores rest waste and hgh qualty organc waste, whch are more expensve for the consumer n terms of money or labor. 14

15 3.3.3 Labor cost organc waste Another parameter that affects the effcency of the polcy change s the actual labor costs of producng low qualty and hgh qualty organc waste. In the benchmark case t s assumed that 0.8 unts of labor are necessary to produce one unt of hgh qualty waste (unts n mllon tonnes) and 0.5 unts of labor to produce one unt of low qualty organc waste. In ths senstvty analyss these costs are vared. However, the proportonal dfference between labor costs of low and hgh qualty organc waste s mantaned. The results are shown n Fgure 4. {enter fgure 4 here} As expected, the lower the labor costs, the hgher the organc waste generaton. Ths means that less rest waste s generated. If the labor costs rse, less rest waste wll be substtuted for both low qualty organc and hgh qualty organc waste. If organc waste s very expensve to produce then almost no rest waste s substtuted for organc waste. The total amount of hgh and low qualty organc waste generated n that case s equal to the benchmark level Income share green consumer The fnal parameter that could have a serous effect on the polcy results s the ncome share of the green consumer. In the benchmark case we assumed that the group of tradtonal consumers s about four tmes larger than the group of green consumers. The green consumer s less lkely to substtute rest waste for low qualty organc waste. If the group of green consumers ncreases n sze, t becomes less lkely that large amounts of rest waste wll be substtuted for low qualty organc 15

16 waste. In such a case, the results of the polcy change wll be completely dfferent. The results of ths analyss are shown n Fgure 5. {enter fgure 5 here} The larger the ncome share of the green consumer s, the lower the amount of low qualty organc waste snce ths consumer s less lkely to substtute low qualty organc waste for rest waste. Ths n turn means that more rest waste s generated. The producton of hgh qualty organc waste s hardly affected by the ncome share, whch s logcal snce the demand for hgh qualty organc waste s nelastc for the green consumer Interacton between labor cost of compostng and substtuton elastcty between low and hgh qualty compost Fnally we have examned the nteracton between the labor cost of generatng organc waste and the substtuton elastcty between hgh and low qualty waste. In Fgure 6 the mpacts on the generaton of rest waste are shown. {enter fgure 6 here} As expected, lower labor cost for producng organc waste results n more organc waste beng produced and therefore lower quanttes of rest waste. The substtuton elastcty between low and hgh qualty waste has only a small effect on the generaton of rest waste n ths case. 16

17 The generaton of low qualty organc waste s more strongly affected by changes n the substtuton elastcty between hgh and low qualty organc waste (see Fgure 7). Gven that the labor cost of producng organc waste s small, the substtuton elastcty between hgh and low qualty organc waste wll greatly affect the amounts of hgh and low qualty organc waste generated. If the substtuton elastcty s low, then only a small amount of low qualty organc waste s generated. If the substtuton elastcty s hgh, then the amount of low qualty organc waste s nearly trpled. If, however, the labor costs of generatng organc waste are hgh, then the substtuton elastcty has hardly any effect on the generaton of low and hgh qualty organc waste. {enter fgure 7 here} 4 Dscusson and conclusons In ths artcle, the effects of ntroducng a unt-based prcng scheme for the collecton of rest waste are analyzed. A general equlbrum model n the Negsh format s presented, wth the possblty of generatng three types of waste. In the model the consumers are gven the possblty of substtuton between three dfferent knds of waste. Wth ths model t s possble to llustrate some mportant aspects of the waste sector and the danger of waste leakage. Waste leakage occurs when households start to dump rest waste n organc waste or other knds of recyclable waste, thus pollutng the recyclable waste stream and makng recyclng or compostng of ths waste stream more expensve or mpossble. 17

18 The results show that ntroducng a unt-based prcng scheme can cause sgnfcant waste leakage. Waste leakage wll greatly nfluence the effectveness of the polcy change. The tradtonal consumers who have lttle preference for the envronment have strong ncentves to dump part of ther rest waste n the organc waste stream, thereby creatng low qualty organc waste, whch wll be more dffcult to compost. The senstvty analyss shows that these results are qute senstve to several parameters n the model. The labor cost of generatng organc waste wll especally nfluence how much rest waste s substtuted for (low qualty) organc waste. The substtuton elastctes between low and hgh qualty organc waste and the substtuton elastcty between organc waste and rest waste wll also nfluence the effectveness of the polcy. Fnally, the ncome share of the green consumer has a sgnfcant mpact on the results. The envronmental concerns of these consumers wll gve them a dsncentve to dump rest waste n organc waste. Therefore, the larger the group of green consumers the smaller the problem of waste leakage. Waste leakage wll greatly ncrease the cost of compostng and could even make t fnancally unattractve or mpossble to compost waste. The result could be a stuaton where all organc waste s ether ncnerated or landflled. Whle decdng to mplement a unt-based prcng scheme or any other scheme where the consumers are punshed for the amount of rest waste they produce, the danger of waste leakage should be taken nto account. Especally larger muncpaltes and mega-ctes, whch tend to have a larger share of tradtonal consumers, wll have to estmate the mpacts of waste leakage and potental costs to prevent these knds of counter productve effects. 18

19 Notes 1 We would lke to acknowledge useful comments of Tmo Kuosmanen on prevous versons of ths paper. Ths paper s part of the project: materal use and spatal scales n ndustral metabolsm fnanced by the Netherlands Organzaton for Scentfc Research. 2 Correspondng author, tel fax , e-mal: Heleen.Bartelngs@alg.shhk.wau.nl. 3 In a unt-based prcng scheme households pay a varable fee for the collecton of waste, where the total amount of the fee depends on the actual quantty of waste generated. 4 In a flat fee prcng scheme consumers are charged a fxed fee ndependent of the amount of waste they actually produce. 5 General knowledge of AGE models n the Negsh format s assumed. For more nformaton about general equlbrum modellng n the Negsh format see for example Negsh (1972) or Gnsburgh and Keyzer (1997). 6 Labor supply equals the exogenously determned labor endowment mnus the labor used by prvate households to generate organc waste. 7 In a flat fee prcng scheme consumers pay a fxed amount of money for the collecton of waste, whch s ndependent of the actual amount of waste that s produced. Therefore the margnal cost of producng one unt of waste s equal to zero. 8 A drect tax only nfluences the ncome of the consumer and does not nfluence n anyway how the ncome s spend. 9 To nclude the subsdy-cum-tax scheme n the model the total cost of the per unt subsdy (ξ) on waste collecton of both rest waste (ξ r TW r ) and organc waste (ξ o TW o ) has to be added to the total welfare functon due to techncal reasons. Therefore the welfare functon used n the model s the followng: r r c c TW = α ln( u ) + ξ TW + ξ TW Addng the subsdy term to the total welfare functon s solely done to change the margnal prces of waste collecton. For more nformaton on ths subject see Gnsburgh and Keyzer (1997). 10 Implctly ths means that part of the used materal wll accumulate n the stock of durable goods. Therefore at a gven moment of tme the materal nflow does not have to be equal to the materal outflow n the model. 11 The notaton z=ces(x,y;σ) reflects the followng functon: σ ( 1 σ) ( 1 σ) 1 σ σ σ z = x + y 12 The varables shown n these equatons are all k x 1 vectors, where k stands for all commodtes n the model. 13 By takng the margnal value of the balance constrant, the prce vector p can be determned (ths s symbolzed by p). The prce vector s used n calculatng the budget constrant and n determnng the Negsh weghts. 14 The column of each producer sums to zero to ensure that the zero proft condton holds (value of nput equals value of output). The column of each consumer sums to zero to ensure that the budget constrant holds (consumers spend exactly ther ncome on the consumpton of goods and servces). Each row must sum to zero n order to ensure that each market clears (total demand for each commodty must equal total supply). 15 As mentoned n secton 2, to nclude the subsdy-cum-tax scheme n the model the total cost of the per unt subsdy (ξ) on waste collecton of both rest waste (ξ r TW r ) and organc waste (ξ o TW o ) has to be added to the total welfare functon due to techncal reasons. Ths s solely done to change the margnal prces of waste collecton. For more nformaton on ths subject see Gnsburgh and Keyzer (1997).. 19

20 Appendx A. Specfcaton of relevant equatons A1.1. Model specfcaton a fxed fee for the collecton of organc and rest waste Welfare Total welfare functon: r r c c (2.10) TWF = α ln( u ) + ξ TW + ξ TW Where utlty consumers depend on the consumpton of the consumer good 15 u x For = (2.11) g To ensure that organc waste s generated n the benchmark case, two fctonal consumers are ntroduced, who only derve benefts from the generaton of organc waste: u g x x ol, oh, (, ) for = 4,5 (2.12) Producton functon goods and collecton servces j j j j q CES( k, l ; σ kl ) = for each j (2.13) Market clearance Goods market balance: x q p g g g (2.14) Captal market balance: j j k k K p (2.15) Labor market balance: j l l L p j (2.16) Where labor supply s determned by: L L lw f = for = (2.17) f Collecton rest waste market balance: 20

21 x TW p r r r t (2.18) r r r TW q p (2.19) Collecton organc waste market balance: x + x TW p (2.20) ol, oh, o o t o o o TW q p (2.21) Waste equatons Waste generaton as percentage consumpton: W = β x g (2.22) W CES x CES x x σ σ x r o, l o, h lh ro = (, (, ; ); ) µ lw o, f f f (2.23) (2.24) Calculaton Negsh weghts Budget constrant consumer : p K + p L F LST = p x + p x + p x for =1,2 k l g g r r c c t t (2.25) Budget constrant government: p K + F T + LST = p x for =3 k g g (2.26) Total expendture government s kept constant at benchmark level. If expendture would change for any reason, then the ncome of the government s compensated through lump sum transfers. Where: o k LST = Y ( p K + F T) gov for = 3 (2.27) Total cost subsdy calculated as a lump sum transfer: (2.28) T = ξ x + ξ x r r o o, f f A1.2. Model specfcaton ncludng a unt-based prcng scheme for the collecton of rest waste 21

22 In the unt-based prcng scheme model the followng equaton are changed: Total welfare functon: c (2.29) c TWF = α ln( u ) + ξ TW Market balance constrant for collecton rest waste: x q p r r r (2.30) Budget constrant consumer : p K + p L F LST = p x + p x + p x for = 1,2 k l g g r r c c t (2.31) Where fee refers to the fee for collecton of organc waste only. Budget constrant government: for = 3 p K + F T + LST = p x k g g (2.32) Total cost subsdy on collecton of organc waste calculated as a lump sum transfer: T cc c, f = ξ x (2.33) f Appendx B Defnton of ndces, parameters and varables Indces Label Entres Descrpton f qualty organc waste (low, hgh) consumers j goods (consumer good g, collecton servce rest waste r, collecton servce compost waste c) z commodtes (goods, captal and labor) Parameters n GAMS specfcaton Symbol Descrpton α Negsh weght β waste percentage µ labor cost for generatng organc waste σ kl substtuton elastcty between labor and captal σ lh substtuton elastcty between low and hgh qualty organc waste substtuton elastcty between rest waste and organc waste σ rc 22

23 ξ F K L LST P p t T Y 0 subsdy wedge flat fee for waste collecton endowment of captal endowment of labor lump sum transfer to keep ncome of government constant prce prce ncludng subsdy transfer cost subsdy ntal ncome Varables n GAMS specfcaton Symbol k l lw q TW TWF u W x Descrpton captal use labor use labor use for generaton of organc waste producton total demand for waste collecton servces total welfare utlty total generaton of waste consumpton References Choe, C. and I. Fraser (1999) An economcs analyss of household waste management. Journal of Envronmental Economcs and Management 38, Fullerton, D. and T.C. Knnaman (1995) Garbage, Recyclng and llct burnng or dumpng. Journal of Envronmental Economcs and Management 29, Fullerton, D. and T.C. Knnaman (1996) Household demand for garbage and recyclng collecton wth the start of a prce per bag. Amercan Economc Revew 86, Fullerton, D. and W. Wu(1998) Polces for green desgn. Journal of Envronmental Economcs and Management 36, Gnsburgh V. and M. Keyzer (1997) The structure of appled general equlbrum models. London: The MIT Press. 23

24 Hong, S. R., Adams, M., and Love, H. A.(1993) An economc analyss of household recyclng of sold waste: the case of Portland, Oregon. Journal of Envronmental Economcs and Management 25, Lnderhof, V., P. Kooreman, M. Allers and D. Wersma (2001) Weght-Based Prcng n the Collecton of Household Waste; the Oostzaan Case, Resource and Energy Economcs 23, Jenkns RR (1993) The economcs of sold waste reducton, the mpact of users fees. Aldershot: Edward Elgar. Mranda, M. L., J.W. Everett, D. Blume and A.R. Barbeau Jr. (1994) Market-based ncentves and resdental muncpal sold waste. Journal of Polcy Analyss and Management 13 (4), Negsh, T. (1972) General equlbrum theory and nternatonal trade. Amsterdam: North-Holland publshng company. Palmer K. and M. Walls (1997) Optmal polces for sold waste dsposal taxes, subsdes, and standards, Journal of Publc Economcs 65, Statstcs Netherlands (1998) Natonal accounts of the Netherlands. Voorburg: Statstcs Netherlands. Sterner, T. and H. Bartelngs (1999) Household waste management n a Swedsh muncpalty: determnants of waste dsposal, recyclng and compostng. Envronmental and Resource Economcs 13,

25 Producton Goods Consumpton Waste Organc waste: low qualty Organc waste: hgh qualty Rest waste Collecton of organc waste Collecton of rest waste Fgure 1 Representaton of the basc model 25

26 Table I Benchmark accountng matrx (expendtures n 100 mllon NLG, 1996) Good CS rest CS organc Cons1 Cons2 Gov Colsum Prce Good CS rest CS compost Captal Labor Fee Subsdy Rowsum Note: Good stands for the consumpton good; CS rest stands for collecton servces of rest waste, CS organc ndcates collecton servces of organc waste; fee s the flat fee consumers pay to the government for collecton of waste, subsdy stands for the total amount of money the government gves for collecton of waste as a subsdy to the consumers. The prce column gves the prces of all commodtes; Rowsum s the sum of a column, Colsum s the sum of each row. 26

27 Table II Addtonal data about the generaton of organc waste n the benchmark Cons1 Cons2 Low qualty organc waste generated (mllon tonnes) Hgh qualty organc waste generated (mllon tonnes) Share of low qualty organc waste n total amount organc waste 25% 10% Unts of labor necessary to generate 1 mllon tonnes of low qualty organc waste Unts of labor necessary to generate 1 mllon tonnes of hgh qualty organc waste Total labor unts spent on compostng

28 Table III Substtuton elastctes for producton factors and waste categores Good CS rest CS organc Cons1 Cons2 Substtuton elastcty between captal and labor (σ k,l ) Substtuton elastcty between organc waste and rest waste (σ o,r ) Substtuton elastcty between hgh and low qualty compost (σ h,l ) Note: Good stands for the consumpton good; CS rest stands for the collecton of rest waste and CS organc stands for the collecton of organc waste. Note 2: See secton 2 for an explanaton of each of the substtuton elastctes 28

29 Table IV Results for man varables for the flat fee and unt-based prce (n brackets % change as compared to flat fee) Flat fee Unt-based fee Cons1 Cons2 Cons1 Cons2 Consumpton good (-0.05%) (-0.06%) Collecton rest waste (-46.55%) 1.47 (-3.29%) Collecton organc waste (185.53%) 0.43 (13.16%) 29

30 Table V Addtonal results organc waste for the flat fee and unt-based prce (n bracket % change as compared to flat fee) Flat fee Unt-based fee Cons 1 Cons2 Cons1 Cons2 Amount low qualty organc waste (623.68%) (39.47%) (mllon tonnes) Amount hgh qualty organc waste (39.65%) (10.82%) (mllon tonnes) Share low qualty organc waste 25% 10% 63% 12% 30

31 8 7 waste (mllon tonnes) Rest waste Low qualty organc waste Hgh qualty organc waste Index for sub. elas. between rest waste and organc waste (benchmark=1) Fgure 2 Senstvty analyss for the substtuton elastcty between rest waste and organc waste: mpacts on quanttes of waste note: The substtuton elastcty s calculated as the benchmark substtuton elastcty multpled by a certan factor, where the value of the factor s shown on the x-axs. 31

32 6 Waste (mllon tonnes) Rest waste Low qualty organc waste Hgh qualty compostable waste Index for sub. elas. between hgh and low qualty organc waste (benchmark=1) Fgure 3 Senstvty analyss for the substtuton elastcty between low and hgh qualty organc waste: mpacts on quanttes of waste 32

33 Waste (mllon tonnes) Index for labor cost organc waste (benchmark=1) Rest waste Low qualty organc waste Hgh qualty organc waste Fgure 4 Senstvty analyss labor cost organc waste: mpacts on quanttes of waste 33

34 Waste (mllon tonnes) Index for change ncome share green consumer (benchmark=1) Rest waste Low qualty organc waste Hgh qualty organc waste Fgure 5 Senstvty analyss for the ncome share of the green consumer: mpacts on quanttes of waste 34

35 8 7 6 Rest waste (mllon tonnes) Index for labor cost 1.8 organc waste (benchmark=1) Index for sub. elas. hgh low qualty organc waste (benchmark=1) Fgure 6 Interacton between labor cost and substtuton elastcty between hgh and low qualty: mpacts on quantty of rest waste 35

36 7 6 5 Low qualty organc waste (mllon tonnes) Index for labor cost organc waste (benchmark=1) Index for sub. elas. between hgh and low qualty organc waste (benchmark=1) Fgure 7 Interacton between labor cost and substtuton elastcty between hgh and low qualty: mpacts on quantty of low qualty organc waste 36