Waste, recycling, and “Design for Environment”: Roles for markets and policy instruments

Resource and Energy Economics 27 (2005) 287–305 www.elsevier.com/locate/ree

Waste, recycling, and ‘‘Design for Environment’’: Roles for markets and policy instruments Paul Calcott a,
, Margaret Walls b a

Faculty of Commerce and Administration, School of Economics and Finance, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand b Resources for the Future, 1616 P St., N.W. Washington, DC, USA

Received 2 June 2003; received in revised form 19 January 2005; accepted 3 February 2005 Available online 15 April 2005

Abstract Households sometimes have two recycling options. Curbside recycling collections are convenient, but do not provide payment. Alternatively, payment might be available from ‘reverse vending machines’ or drop-off centers, but some transaction costs would be incurred. We examine policies to encourage efficient product design and recycling in a setting with these two recycling options plus the option of putting recyclables in the trash. We find value in having two parallel recycling options. Constrained optimal outcomes can be attained by combining a ‘deposit–refund’ with a modest disposal fee. Furthermore, producers should not be permitted to keep deposits, that are not claimed by consumers. # 2005 Elsevier B.V. All rights reserved. JEL Classification: H21; Q28 Keywords: Recycling; Design for environment; Solid waste

1. Introduction Solid waste policy should provide correct incentives for both ‘‘upstream’’ and ‘‘downstream’’ decisions. Upstream, it should encourage product design to reflect environmental concerns, and downstream it should encourage recycling, diverting solid waste from landfills.


Corresponding author. Tel.: +64 4 463 6585; fax +64 4 463 5014. E-mail addresses: [email protected] (P. Calcott), [email protected] (M. Walls).

0928-7655/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.reseneeco.2005.02.001

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Incentives for efficient recycling have been addressed in a range of papers. The simplest approach is for consumers to pay a fee for waste disposal that reflects its full social cost. A combined output tax and recycling subsidy, often referred to as a deposit–refund, can also provide incentives to recycle, and has the advantage that it does not encourage illegal dumping (Dinan, 1993; Sigman, 1995; Fullerton and Kinnaman, 1995; Palmer and Walls, 1997). It is also possible to impose both a tax–subsidy combination and a disposal fee. In general, the disposal fees that consumers pay and the environmental tax that producers pay per item of trash produced (an ‘‘advance disposal fee’’) should combine to equal the social cost of waste disposal (Choe and Fraser, 2001; Shinkuma, 2003). The issue of upstream ‘‘Design for Environment’’ (DfE) is becoming increasingly important to environmentalists and to environmental policy makers. In the same way that the pollution policy focus is shifting from so-called ‘‘end-of-pipe’’ treatments to pollution prevention, solid waste policy is shifting from waste disposal concerns back upstream to product and process design issues. This shift is manifested in the concept of ‘‘extended producer responsibility’’, or EPR – the notion of making producers physically or financially responsible for products at the end of the products’ useful lives (see http:// www.epa.gov/epr/). EPR laws, which sometimes mandate that producers take back products for recycling, have been passed for packaging, electronics, home appliances, and automobiles in many European countries, Japan and elsewhere. Fullerton and Wu (1998) were the first to address DfE in an economic model. They assumed that producers choose an amount of packaging for their products and a degree of recyclability, where recyclability is the fraction of the product that can be recycled. They then solved for optimal policies under a range of different assumptions about missing markets and the feasibility of various policy instruments.1 Efficient DfE requires incentives for producers to design products that are easily recycled. Such incentives would be generated by fully functioning markets for recyclables, whereby recyclers pay consumers a price for their used products that depends on the degree of recyclability. Alternatively, such incentives could be provided by a tax–subsidy combination (a deposit–refund scheme), if taxes and subsidies were customized to the recyclability of each specific product. In an earlier paper (Calcott and Walls, 2000), we argued that neither source of incentives – fully functioning markets or taxes that vary with product recyclability – can be relied on in the real world. As a result, the first-best outcome would be unattainable. We modeled recycling collection at the curbside, in which consumers received no payment for leaving their recyclables at the curb. We found a constrained optimum, and showed how it could be implemented with a modified version of the deposit–refund. The refund – in this case a subsidy to cover the costs of curbside collections – was not set to equal the social cost of waste disposal as in earlier accounts, but to ensure that the (constrained) efficient set of used products would be accepted by recyclers. Previous studies have assumed that recycling markets operate perfectly or (as in our earlier paper) that they do not operate at all. But in reality, recycling markets operate to some extent, they just come with transaction costs. In the current paper, we explicitly 1 Choe and Fraser (2001), in an extension of the Fullerton and Wu model, show that results change somewhat if households can undertake waste reduction activities.

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model these costs.2 Market exchange of recyclables is assumed to be costly, because it requires recyclers to determine how valuable products are for recycling and pay a price based on that value. Consumers may also incur costs in making items available to recyclers. These costs have two consequences in our model. First, consumers may be deterred from selling some of their used products to recyclers, and hand them over for free instead, such as in a curbside recycling bin. Other used products will be valuable enough, however, so that it is worthwhile to incur transaction costs. Consumers will receive a payment for these products; a payment which depends on how valuable that product is for recycling. Remaining items, on which recyclers would incur a loss, are put in the trash. If transaction costs are heterogeneous, then there is a second consequence. Consumers will vary in how much they recycle. They will not always sort their used products into recyclables and non-recyclables. For example, some consumption takes place away from home where recycling is less convenient, leading to the product ending up in the trash. Some evidence suggests that this phenomenon is increasing in the U.S. Aluminum cans, collected in every curbside recycling program in existence and widely recognized as the most profitable material in the waste stream to recycle, has experienced declining recycling rates in recent years. Gitlitz (2002) reports that less than half the cans on the U.S. market in 2001 were recycled. This compares to a recycling rate of 65% at the peak in 1992. We use our model to identify policy settings that implement (constrained) efficient recycling and design decisions. We address three questions about the design of such tax– subsidy schemes targeted at recycling markets: (1) whether such schemes need to be accompanied by regulations such as a take-back mandate, (2) whether such schemes are necessary for recycling markets even where curbside recycling is available, and (3) who should keep unclaimed deposits—the manufacturer or the state. We now discuss each of these questions in turn, and note the answers suggested by our model. Deposit–refund schemes sometimes impose regulations as well as taxes and subsidies. For example, some states in the U.S. have passed ‘bottle-bills’ which set up a system of deposit–refunds for beverage containers, but also mandate the amount that consumers should receive for their returned items, and which organizations are required to accept returned items. In Germany, a deposit–refund system exists for beverage containers in addition to an extensive take-back program that covers not only beverage containers but a wide variety of other consumer products as well. We examine whether these kinds of regulation are necessary, or whether recycling and design decisions can be implemented purely with incentives—taxes, subsidies and disposal fees. We show that environmental goals can be achieved with incentive-based policies alone, even in the realistic setting that we assume. The existence of markets, even imperfect ones, and the use of relatively simple policy instruments go a long way toward encouraging DfE. To some extent, curbside recycling provides a substitute for drop-off centers where consumers are paid for their recyclables. To this extent, there is a question about whether both are required. When the bottle-bills were introduced, curbside recycling was not very 2 Shinkuma (2003) does assume transaction costs, but they are associated with the operation of a deposit–refund scheme rather than with markets per se. In addition, Shinkuma does not address the possibility that recycling can be collected from the curb to reduce transaction costs, and consequently does not address the policy questions dealt with below.

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extensive. The spread of curbside recycling has led to questions about whether bottle-bills should be phased out (McCarthy, 1993). Because our model includes both types of recycling, we are able to address this issue directly. Although payment to consumers for their recyclables does have costs, which may be prohibitive for low value items such as newspapers, we can identify two benefits from payment. First, more recyclable products can be sold to recyclers for higher prices at the end of life, and hence consumers will be willing to pay more for them during the original purchases. This provides an incentive for producers to design more recyclable products. Second, payment to consumers leads to a higher recycling rate. As our model acknowledges, some recyclable products are not actually recycled. As a consequence, a deposit paid on such a product will not be refunded to the consumer. Unclaimed deposits could be retained by manufacturers, appropriated by the state or divided between them. Each of these options has been adopted in at least one bottle-bill state, and the issue is often a very contentious one.3 We show that in order for the constrained optimum to be implemented, manufacturers must lose unclaimed deposits. The reason is that manufacturers need some penalty for producing goods that will end up in landfills. In a first-best world, this penalty could be provided by fees charged to consumers for waste disposal, conveyed upstream to the producers by product markets. But because of the missing price for curbside recycling, disposal fees must be set according to another criterion—giving consumers correct incentives about when to recycle. The model is outlined in the following section. We characterize an equilibrium with perfect sorting of recyclables in Section 3. In Section 4, we show how a constrained optimum can be attained with a range of policy settings— including an option which only requires taxes and subsidies. However, in this model it is not necessary to apply a deposit– refund to recycling markets. Consequently, Section 4 does not provide a compelling rationale for interventions such as bottle-bills. Our rationale, and our answer to the third policy question, follow from some recyclable items ending up in landfills. We introduce this incomplete sorting as an equilibrium phenomenon in Section 5, and derive unique values of the deposit–refund and disposal fee that implement the constrained optimum. Section 6 provides concluding remarks.

2. The model 2.1. Characterization of recyclability We adopt a simple and general characterization of product recyclability. The degree to which a product is recyclable is represented with the scalar index r, which determines the cost of recycling the product. This treatment of recyclability follows Calcott and Walls (2000), but differs from that of Fullerton and Wu (1998) who interpret recyclability as the 3 In New York, bottlers get the unclaimed deposits; in Michigan, 75% goes to the state and 25% back to retailers. The state legislature in New York has recently considered changing the law to get access to the deposits which sources estimate are between US$ 85 million to US$ 140 million annually (Santora, 2004).

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proportion of a product that can be recycled.4 Although neither interpretation is strictly correct for all products, we feel that the cost approach is more realistic for many goods. Almost any product is technically recyclable, but many products are prohibitively costly to recycle. And most changes that producers can make to a product do not increase the proportion of an individual product that is recycled, but rather lower the cost of recycling the product. These changes are wide-ranging. For example, the cost of recycling plastic packaging is lower if contaminants that cannot be readily separated from the packaging are avoided, if particular types of plastics are avoided, and if particular production methods are used. Electronic products can be designed to ease disassembly; suitable labeling of materials can also make recycling easier and less costly.5 A wide range of these activities is allowed for in our model. Our view of recyclability leads us to pessimism about the prospects for taxes or subsidies on producers to provide correct incentives for DfE. Recyclability is often too complicated for policymakers to measure meaningfully, and so tax reductions cannot accurately reward producers for increasing the recyclability of their products. If recyclability was just the proportion of a product that is composed of a certain material, as other authors have assumed, then upstream design incentives would be more feasible. We assume a composite material input. Consequently, some increases in recyclability that result from using more environment-friendly inputs will not be explicit in the model.6 In Appendix D, we present an extension that allows for multiple types of material inputs. Our basic findings continue to hold, however, and because the model with multiple inputs is significantly more complicated to present, we limit it to Appendix D. 2.2. Agents and technologies We develop a simple model that incorporates four stages in the product life cycle and two types of resource. The stages are extraction of virgin materials, production, consumption and removal; either recycling or disposal. The first type of resource is material and the second is non-material. Fig. 1 gives an illustration of the model. Each node in Fig. 1 represents a different activity. The direction of the arrows indicates the flow of materials, and the price in each of the markets is shown along the arrows. Our focus is on DfE and recycling. Consequently, we make simple assumptions about waste disposal and virgin material extraction. Private waste collection and disposal costs per unit are constant and equal to g D . The extraction of virgin materials is assumed to be conducted in a competitive industry, characterized by constant returns to scale. The perpound extraction cost is g E . 4 Eichner and Pethig (2001) treat recyclability as a proportion—in this case the proportion of a product’s material content that is of a particular type. Choe and Fraser (1999) model producers as choosing the ‘‘waste content’’ of their products. 5 For a good discussion of these issues and more about DfE, see Fiksel (1996), especially Chapter 8, U.S. Congress Office of Technology Assessment (1992), and American Plastics Council (2001). 6 Improved recyclability sometimes requires producers to change the mix of materials used in production— making a container out of glass rather than plastic, for example, or out of a single plastic resin rather than a mix of resins.

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Fig. 1. The flow of materials.

In the production stage, each firm u uses vðuÞ pounds of newly extracted virgin materials and rðuÞ pounds of recycled inputs to produce a material output. These two types of material input are perfect substitutes in production. We normalize the product weight to one pound per item. As a result, firm u’s total output has a mass of qðuÞ, equal to the number of items it produces. There are no waste by-products generated during production.7 This leads to a materials balance condition given by: vðuÞ þ rðuÞ ¼ qðuÞ. Production also requires a non-material input. The amount of this input that firm u requires to produce q units with recyclability r is represented with the cost function cðr; q; uÞ. Increasing output or recyclability increases non-material costs. Thus, cq > 0 and cr > 0, where subscripts denote first partial derivatives. We also assume that average costs are increasing in r.8 R Consumers are homogeneous with quasi-linear utility function Vð qðuÞdu; WÞ þ m.9 Utility depends on consumption of the material good, aggregate solid waste generated by all consumers, W, and consumption of the non-material numeraire good, m. Consumers consider different varieties of material output to be perfect substitutes, and so utility does not depend directly on how much each producer contributes to consumed output. Aggregate waste disposal, W, has a negative effect on utility. Consumption does not use up any materials. All consumed materials must be removed at the end of product life. There are three methods of removal: waste disposal, collection of recyclables at the curbside, and sale of recyclables to a ‘reverse vending machine’ or a drop-off center.10 Products removed by the latter two methods are recycled and used again in production. The remaining materials, with aggregate mass W are sent to landfills. 7 These assumptions could be relaxed, but it would not change our basic results and only serve to clutter the model. Calcott and Walls (2000) and Calcott and Walls (2002) treat product weight as a choice variable. Palmer and Walls (1997) and Walls and Palmer (2001) allow for a manufacturing by-product, although they do not consider product design. Walls and Palmer (2001) also consider the case of some air or water pollution generated during the production process. 8 Formally, if q
ðr; uÞ is the profit maximizing output for u if it chooses r, then we assume that cðr; q
ðr; uÞ; uÞ=q
ðr; uÞ is increasing in r. 9 Nothing but notational economy would be lost by permitting consumers to differ in their utility functions, Vð; Þ. There are a continuum of consumers with a unit mass. 10 Consumers may receive payment from reverse vending machines (for drink containers), at recycling centers, from materials brokers, and from end-users such as paper mills.

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We assume a steady state. In such a state, the amount of recycled material used in production is the same as thatR generated by recyclers, and as much material leaves the system as enters it, i.e., W ¼ vðuÞdu. In processing a product with recyclability r, the recycler incurs a constant cost per item, kðrÞ, in the recycling process, where k0 ðrÞ < 0 and k00 ðrÞ > 0, i.e., increasing recyclability of a product reduces the costs of recycling, but at a declining rate. Finally, there are non-material transaction costs associated with each form of disposal. The transaction cost of waste disposal is normalized to zero. T2 is the transaction cost associated with recycling, and there is an additional cost, T3 associated with payment to consumers, which is above and beyond any transaction costs associated with collection of recyclables for free. For simplicity, we begin by assuming that this transaction cost is borne directly by the consumer. However, it is important to realize that this simplification is not a substantive restriction. In Section 3, we will also account for costs incurred by recyclers when they pay for recyclable items. 2.3. Policies and markets This paper focuses on distortions to DfE and recycling due to transaction costs in recycling markets. We assume there are no other distortions due to income or other taxes, or to non-competitive markets. We require some further assumptions to deliver competition in the product market. If some products are to be recycled and others are to be landfilled, then firms must design products with a range of levels of recyclability. We allow for this by assuming that firms have heterogeneous cost functions. Clearly, we do not want this heterogeneity to endanger the competitiveness of the product market. We assume that a firm’s technology cannot be imitated by its rivals, and that average costs are ‘‘u-shaped’’ with diseconomies of scale that inhibit any firm with a cost advantage from expanding to the point where it would attain market power. One objective of this paper is to demonstrate that incentive-based policies are capable of delivering DfE and recycling. With this objective in mind, we restrict intervention to the setting of policy instruments such as product taxes, recycling subsidies, and disposal fees. In particular, there is no government provision of recycling services; rather recyclers are profit maximizing firms operating in a competitive industry.11

3. Market equilibrium In order to characterize an equilibrium, we work backward through the stages in Fig. 1, recursively substituting prices back into earlier decisions. First, we identify the equilibrium 11 There are a variety of arrangements in the real world (Walls et al., 2002). Local government employees sometimes collect recyclables from households, operate processing centers, and/or sell processed secondary materials. However, often one or all of these operations are contracted out to private firms. And sometimes the government intervenes only by licensing firms to collect materials from households, with processing undertaken by private firms. The purpose of this paper is to examine the prospects for decentralized design and recycling decisions, and efficient tax and subsidy policies in such setting.

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price for materials that recyclers receive from manufacturers. Because recycled and virgin materials are perfect substitutes, and because extraction is a competitive industry, the price per item of recycled materials will be the same as the extraction cost per pound, g E . Recyclers may also receive payment from the government in the form of a recycling subsidy. We let this subsidy vary according to whether the recyclable materials are collected curbside with no payment or collected at reverse vending machines or recycling centers where payment is made; s2 is the subsidy for curbside recycling and s3 is the subsidy for other recycling.12 Recyclers pay consumers pr ðrÞ for recyclable materials that are brought to reverse vending machines or recycling centers and also incur costs of kðrÞ. In this setting, a recycler makes a net gain of g E  kðrÞ þ s3  pr ðrÞ on every pound of material with recyclability r that it processes. Under the assumption that recyclers are perfectly competitive and have no fixed costs, each recycler will make zero profits on each purchase. This means that the equilibrium price that consumers receive from recyclers is pr ðrÞ ¼ g E  kðrÞ þ s3 :

(1)

Some products may be left at the curb for recyclers to collect without payment. Only products that a recycler will not make a loss on, even when paying a price of zero, will be accepted. Such products must have a level of recyclability, r, such that g E  kðrÞ þ s2  0. Let r be the threshold level of recyclability, below which products will not be collected for recycling. Consumers have three ways to have their used products removed, waste disposal, curbside recycling and sale of recyclables at centers and reverse vending machines. They will choose the lowest cost way to get rid of products they have consumed. To begin with, we assume that transaction costs associated with curbside recycling are less than those of disposal, i.e., T2 < 0, and that there is a non-negative fee, f, per pound for garbage collection. This means that transaction costs do not inhibit curbside recycling. A consumer will always prefer to leave a product to be collected for recycling (without payment), than to leave it for the refuse collection. However, recyclers must be willing to accept the product, i.e., it must meet the threshold, r, defined above. If the product has a very high level of recyclability, the consumer will be willing to incur an additional transaction cost T3 , in order to receive payment for it. This means that there is a second threshold, r, ¯ where the price received just offsets T3 , i.e., where g E  kðrÞ þ s3 ¼ T3 . In between these two thresholds, the recycler will accept the item without payment, thus the consumer will choose this method of removal rather than pay the disposal fee. Below the lower threshold, r, the item goes in the trash. Let PRC be the net private removal cost of a product incurred by the consumer at end of product life, 8 if r < r; < f PRCðrÞ ¼ T2 if r  r < r; ¯ (2) : T2 þ T3  pr ðrÞ if r¯  r; 12 We allow the subsidy on curbside recycling, s2 , to differ from the rate on other recycling. But it will turn out that the two rates should be set equal to each other, i.e., that s2 ¼ s3 .

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Fig. 2. Private removal costs.

where r ¼ min frjg E  kðrÞ þ s2  0g

and r¯ ¼ min frjg E  kðrÞ þ s3  T3 g:

(3)

So long as s3  s2 < T3 , r¯ will be higher than r as defined in Eq. (3), and so there will be a range of values of r between these thresholds. Therefore, there could be products which would be collected for recycling at the curb. PRC is illustrated in Fig. 2, as the discontinuous bold curve, under the assumption that s2 ¼ s3 . It has three sections, as identified in Eq. (2), separated by the thresholds. This figure also illustrates the determination of the two thresholds. The lower threshold, r, marks the discontinuity in PRC, where pr ðrÞ ¼ 0, i.e., where T2 þ T3  pr ðrÞ ¼ T2 þ T3 . The higher threshold, r, ¯ marks the kink in PRC where pr ðrÞ ¼ T3 , and thus PRCðrÞ ¼ T2 . Consumers take PRC into account when deciding how much and which variety of product to consume. They choose quantities, qðuÞ of each firms’ output to maximize utility, R Vð qðuÞdu; WÞ þ m, subject to the constraint that gross expenditure: Z ðPq ðrðuÞÞqðuÞ þ qðuÞPRCðrðuÞÞÞdu þ m; (4) does not exceed income. The first order conditions generate an inverse demand curve for material goods. If producer u designs its product to have recyclability r, then it will face an inverse demand curve given by Eq. (5): (5) Pq ðrÞ ¼ V¯ q  PRCðrÞ; where V¯ q ¼ @Vðq; WÞ=@q is the willingness to pay for another unit of the material good.

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Producers internalize the PRC of their products, because if the consumer anticipates a higher removal cost, she will pay a lower price for the product. Producers also bear other costs. As explained above, they pay price, g E , per pound for material inputs. They may also pay an output tax. We allow the output tax to depend on whether a product is accepted for recycling without payment – in a curbside program – and whether it is paid for, say at recycling centers. There are thus three tax rates, t1 , t2 and t3 , levied on non-recyclable products, products eligible for curbside recycling and products paid for by recyclers respectively.13 Adding taxes and input prices to the PRC, we obtain a single expression for Private material cost (PMC): 8 if r < r; < f þ g E þ t1 if r  r < r; ¯ (6) PMCðrÞ ¼ g E þ t2 þ T2 : ðt3  s3 Þ þ T2 þ T3 þ kðrÞ if r¯  r; where r and r¯ are as defined in Eq. (3). Producers also incur some non-material costs of production, cðr; q; uÞ. Producer u chooses its output quantity, q and recyclability, r, to maximize profits. Using the inverse demand function above, and the definition of PMC, the profit function can be written as (7) ½V¯ q  PMCðrðuÞÞqðuÞ  cðrðuÞ; qðuÞ; uÞ: Note that PMC is not always strictly increasing in r, and so the producer does not always get a benefit from increasing recyclability. PMC only increases in r when such an increase means that the product become eligible for the curbside collection of recyclables, or when the level of r is above r. ¯ This means that the only levels of r that producers would ever choose are (i) zero, (ii) the threshold level that makes the product acceptable for recycling, and (iii) levels over the second threshold.14 The flat section in PMC, from r to r, ¯ is inherited from PRC. As illustrated in Fig. 2, PRC does not vary as r varies between r and r. ¯ Because no price is paid for curbside recycling, there is no reward for increases in recyclability over this range. PMC is affected by taxes as well as prices. But, as the government cannot measure r, taxes do not provide this reward either. Consequently, no producer would design a product with r strictly between r and r. ¯ To acknowledge that some levels of recyclability are not implementable, we amend the expression for PMC 8 to be if r ¼ 0; < f þ g E þ t1 if r ¼ r; PMCðrÞ ¼ g E þ t2 þ T2 (8) : ðt3  s3 Þ þ T2 þ T3 þ kðrÞ if r¯  r: To solve for optimal policy instruments, we will try to set the private material cost equal to the social cost. We turn to that cost in the following section. But first we note that Eqs. (7) and (8) are consistent with recyclers as well as consumers bearing T3 . If a recycler incurs a 13 In Calcott and Walls (2002), we allow taxes to vary continuously with recyclability, r. Such a policy would be unrealistic in practice. In the present paper, we assume that the government cannot measure recyclability and assess taxes that vary with r, but that it can observe the decisions that recyclers make— decisions that depend on recyclability. 14 These are the only viable solutions to the maximization problem. Otherwise, an interior solution would require cr ¼ 0, which is ruled out by the assumption that cr > 0.

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transaction cost then it will have to reduce pr ðrÞ by this amount to cover costs. As a result, our expression for PRC would not have to be amended further.

4. The constrained social optimum TheZ social planner’s objective is given by the following expression: ð½V¯ q  SMCðrðuÞÞqðuÞ  cðrðuÞ; qðuÞ; uÞÞdu;

(9)

which is derived in Appendix A. The planner chooses { qðuÞ; rðuÞ} to maximize Eq. (9) and to ensure that @Vðq
; WÞ=@q ¼ V¯ q . SMC stands for ‘‘social material costs’’ which include the externalities from 8 waste disposal as well as removal costs: < g E þ g D  VW if r ¼ 0; if r ¼ r; SMCðrÞ ¼ kðrÞ þ T2 (10) : kðrÞ þ T2 þ T3 if r¯  r: Note that Eq. (10) reflects the constraint identified in the previous section, to the effect that ¯ As a result, the no product will be produced with recyclability between r and r. unconstrained optimum will not generally be attainable, and we investigate constrained optima.15 The planner chooses levels for the two thresholds, r and r. ¯ In Appendix B, we show how the two thresholds are chosen. Here, we show the instruments that yield the constrained optimal designs and quantities of products, for given levels of the thresholds.16 For a given choice of r, the subsidy on recycling is determined by the zero profit condition for recyclers: s2 ¼ kðrÞ  g E : (11) Remaining instruments are constrained by the need to reconcile PMC with SMC. Comparing Eqs. (8) and (10), we find that the following conditions must hold: f þ t 1 ¼ g D  VW ;

t2 ¼ kðrÞ  g E ;

t 3 ¼ s3 :

(12)

The first expression in (12) states that the direct disposal fee charged to consumers, f, and the ‘‘advance disposal fee’’ on non-recyclables, t1 , should sum to the social cost of disposal. Either the direct disposal fee or the advance disposal fee could be set to zero, so long as the other was set to the social cost of disposal. The second expression in (12), along with Eq. (11), shows that a tax–subsidy scheme (i.e., a ‘‘deposit–refund’’), is required for items collected at the curb (t2 ¼ s2 ¼ kðrÞ ¯  g E ).17 This deposit–refund should be set equal to the marginal cost of recycling at the lower threshold, r, less the marginal cost of 15 In Calcott and Walls (2000) and Calcott and Walls (2002) we characterize first best optima, and show how they could be implemented if recycling markets were fully functional or taxes could vary with recyclability. 16 The government does not set the thresholds and force private markets to meet them; it chooses taxes and subsidies that simultaneously yield the constrained optimal choices of rðuÞ and qðuÞ and the two thresholds. Even if the thresholds are not set at the ideal levels, the settings of policy instruments shown below will still be constrained optimal given whatever thresholds are chosen. 17 This is the same instrument as that suggested for curbside recyclables in Calcott and Walls (2000).

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extraction, g E . A deposit–refund may also be applied to other recyclables (t3 ¼ s3 ) but it is not necessary (i.e., t3 and s3 can be set to zero). However, when incomplete sorting is added to the model in the following section, a deposit–refund on all recyclables will be necessary to attain the constrained optimum.

5. Incomplete sorting of recyclables In the real world, some items that recyclers would accept, end up being thrown away. This can occur when, for example, consumption takes place away from home and no recycling bin is nearby, or it can occur simply by accident or through forgetfulness. In this section, we modify the model to account for this imperfect sorting. We do so by introducing some uncertainty, at the time of purchase, about the eventual transaction costs of recycling a product. In particular, we will now assume that T2 is random.18 A consumer may buy a highly recyclable item in the expectation that it will be recycled, but contingencies may arise that make it more convenient to dispose of it as trash. Let T2 be drawn from a continuous distribution function, with a support that includes positive values. Let p be the probability that an item will be recycled. This probability depends on the price that the 8 item would receive from recyclers, and hence on r: if r ¼ 0; <0 pðrÞ ¼ Probð f  T2 Þ if r ¼ r; (13) : Probð f  T2 þ T3  pr ðrÞÞ if r  r: ¯ If a product is recyclable enough to meet the higher threshold, r, ¯ then further increases in recyclability are reflected in higher prices, pr ðrÞ, and hence to higher probabilities that the product will be recycled. As the product becomes increasingly valuable, it becomes less likely that the consumer will ‘‘forget’’ to recycle it.19 Policy instruments determine the incentives for both DfE and recycling. First consider DfE. Social material costs are affected by incomplete sorting, since recyclable products have a chance of being thrown away. The components of SMC are set out in Table 1. Products either have a recyclability level of zero, r, or some level of recyclability over r. ¯ These three possibilities are represented by the rows of Table 1. Under our current assumptions, any product with r  r¯ can either be recycled or thrown in the trash. This distinction is represented by the columns. If an item is trashed, then its ex post SMC is g E þ g D  VW , irrespective of r. Therefore, this expression is entered throughout the right- hand side column. Recycling costs, on the other hand, depend on r as described in Eq. (10), and are entered in the left-hand side column. 18 As T2 is incurred with any recycling, this randomness can lead to some recyclable products being put in the trash, both for r ¼ r, and for r  r¯ . We assume that consumers do not know their drawing of T2 at the time of purchase, in order to keep the market structure simple and competitive. 19 This imperfect sorting problem is asymmetric. While it is possible for a recyclable product to end up in the trash, we assume it is not possible for a non-recyclable product to end up being recycled. This is because recyclers are profit-maximizing private firms operating in a competitive industry; if a product’s recyclability level is low enough, the costs of recycling are greater than the revenue earned from sale of the secondary material and the recycler will not willingly accept the product.

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Table 1 Ex post SMC with incomplete sorting r¼0 r¼r r < r¯

Recycled

Trashed

– kðrÞ þ T2 kðrÞ þ T2 þ T3

g E þ g D  VW g E þ g D  VW g E þ g D  VW

Ex ante SMC takes into account the possibility, pðrÞ, that a recyclable item will be trashed. It is presented in the following expression—a generalization of Eq. (10): 8 if r ¼ 0; < g E þ g D  VW SMCðrÞ ¼ pðrÞðT2 þ kðrÞÞ þ ð1  pðrÞÞðg E þ g D  VW Þ if r ¼ r; : pðrÞðT2 þ T3 þ kðrÞÞ þ ð1  pðrÞÞðg E þ g D  VW Þ if r > r: ¯ Producers’ actual design decisions are driven by PMC. As with SMC, ex post PMC depends on the eventual destination of a product. Table 2 is the analog to Table 1. Ex ante PMC is set out in the following amendment to Eq. (8): 8 if r ¼ 0; < g E þ t1 þ f PMCðrÞ ¼ g E þ t2 þ ð1  pðrÞÞ f þ pðrÞT2 if r ¼ r; : g E þ t3 þ ð1  pðrÞÞ f þ pðrÞðT2 þ T3  pr ðrÞÞ if r > r: ¯ To ensure that producers’ decisions about design and production levels will be efficient, the planner should reconcile PMC with SMC. But unlike the setting considered in Section 4, now the planner also needs to worry about consumers’ decisions about how to get rid of consumed products. In Section 4 the planner only needed to set the disposal fee above T2 , to implement efficient recycling. But now policy instruments should reconcile PRC with SRC. SRC (including the externality from waste disposal) and PRC are reported in Tables 3 and 4. The policy settings that implement efficient decisions by both producers and consumers are derived in Appendix C. Unlike the policies suggested in Section 4, these policy settings Table 2 Ex post PMC with incomplete sorting r¼0 r¼r r < r¯

Recycled

Trashed

– g E þ t2 þ T2 ðt3  s3 Þ þ kðrÞ þ T2 þ T3

g E þ f þ t1 g E þ f þ t2 g E þ f þ t3

Table 3 SRC – including the externality – with incomplete sorting r¼0 r¼r r < r¯

Recycled

Trashed

– kðrÞ  g E þ T2 kðrÞ  g E þ T2 þ T3

g D  VW g D  VW g D  VW

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Table 4 PRC with incomplete sorting r¼0 r¼r r < r¯

Recycled

Trashed

– T2 T2 þ T3  pr ðrÞ

f f f

are unique. The balance between direct disposal fees and advance disposal fees was indeterminate in the previous section. But now the additional requirements due to incomplete sorting, determine a specific level for direct disposal fees. The required policy settings are set out in the following expression: t1 ¼ t2 ¼ t3 ¼ s2 ¼ s3 ¼ kðrÞ  g E ;

f ¼ ðg D  VW Þ  ðkðrÞ  g E Þ:

(14)

All products face an output tax equal to the difference between recycling costs (at the lower threshold) and virgin material costs, and receive an equivalent subsidy when recycled. This result provides an answer to the second policy question posed in Section 1. A deposit– refund is beneficial even for highly recyclable items, despite the availability of curbside recycling. The same tax rate is levied on all material goods. Intuitively, all products have the same social cost when trashed, and so it is desirable for them to lead to the same private cost when trashed as well. The disposal fee is the same for all products, and so it is desirable for all products to face the same output tax or deposit. In practice, a common tax rate on all recyclable and non-recyclable products is likely to have additional advantages to those that are explicit in the model. Products that are recyclable in one region of the country, might not be in other regions. The proposed set of instruments is robust to that possibility. Moreover, it should be administratively easier for the government to assess a tax that applies to all products, rather than a tax that only applies to products that are collected for curbside recycling. The solution requires relatively simple policy instruments because markets are allowed to do some of the work of providing incentives for DfE. The tax, subsidy, and disposal fee encourage producers to make products recyclable enough for curbside collection, but the incentive to make products with higher levels of recyclability comes from the existence of markets. In addition, the prices paid in recycling markets encourage higher rates of recycling. So far, the analysis has been based on the assumption that producers lose the deposit for products that end up in landfills. But the third policy design question raised in Section 1 was whether producers should lose the deposit on such items. We can address this question by amending the expression for PMC, as stated in Table 2. Under our previous assumption, that producers do lose unclaimed deposits, t3 , the PMC for a product with r > r¯ was g E þ t3 plus the expected PRC. But if producers keep unclaimed deposits, then they would not lose t3 on items unless those items were recycled. The bottom right entry in Table 2 would be amended to g E þ f from g E þ f þ t3 . But then it would be impossible to reconcile PMC and SMC, and so the constrained optimum could not be attained. This is shown formally in Appendix C.

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The reason why producers should lose unclaimed deposits, is that the direct disposal fee has to be kept below the social cost of disposal, to give consumers incentives to make correct removal decisions when curbside recycling collections are free. This means that the direct disposal fee on recyclable items is too low, i.e., it does not impose a sufficient penalty for throwing recyclable items in the trash. The lost deposits on those items make up for this problem. We now have an answer to our third policy question. Manufacturers cannot be permitted to keep unclaimed deposits if the constrained optimum is to be implemented.

6. Conclusion Decentralized decisions by producers and consumers usually rely on markets to transmit incentives. If recycling markets work perfectly – in other words, if recyclers pay consumers for recyclable items and pay higher prices for items with higher value – then consumers would be willing to pay more up-front for products designed to be recyclable. But in fact, recycling is often collected without payment, and so this transmission of incentives does not always occur. In this paper, we explicitly model an explanation of these ‘‘missing prices’’ – an explanation that has been suggested informally by previous authors – that they are precluded by transaction costs. We assume that consumers have two options for recycling: they may recycle at their curb for free or they may take items to a recycler and receive payment but incur extra transaction costs. We also allow for the possibility that consumers imperfectly sort materials into trash and recycling. Thus, we bring into the conceptual model two realistic imperfections in recycling markets. The model allows us to draw some general conclusions about policy, and make some specific recommendations about the design of deposit–refund schemes. First, we argue that regulation is not necessary. We have not explicitly modeled regulation. But unless it can reduce transaction costs, regulation will not deliver a better result than the constrained optimum characterized above. In particular, mandates which specify the price that consumers receive for recyclables are likely to be counter-productive. Unless these prices exactly match the relative social value of recycling, the result will be incorrect incentives for sorting. Second, we identify a rationale for recycling markets and associated deposit–refunds, even when curbside recycling is available. Although recycling markets may come with transaction costs, the existence of such markets encourages greater DfE and more recycling than there would be with only curbside recycling. When there is incomplete sorting of recyclables – i.e., when some recyclables end up in the trash – a deposit–refund applied to all products, even highly recyclable ones, works along with the disposal fee to attain the constrained optimum. The combination of the disposal fee and a single product tax – i.e., deposit – applied to all products ensures that the same social cost is paid for all items thrown in the trash. The refund encourages consumers to bring recyclable products back for recycling. Third, producers should not be permitted to keep unclaimed deposits. Producers should bear the social costs of disposal for products that end up as trash. But as disposal fees will not reflect all of this cost, producers require a further disincentive—which they will not generally have unless they lose the deposit when recyclable items are disposed of as trash.

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Finally, we find that a modest disposal fee is part of the set of constrained optimal policy instruments. The disposal fee should be set equal to the social costs of disposal less the difference between recycling costs (at the threshold) and virgin material costs. Pricing household waste collection and disposal through what are often referred to as ‘‘pay-as-youthrow’’ programs, are becoming increasingly common across the U.S. and in other countries (Miranda et al., 1998, 1994; Linderhof et al., 2001). In practice, a ‘‘modest’’ disposal fee – i.e., something less than the marginal social costs of disposal – may be desirable for reasons outside of our model framework. It could provide incentives for low-cost waste-reduction activities by households, such as leaving lawn clippings on the lawn and composting yard waste, while not creating big incentives for illegal dumping (Choe and Fraser, 1999, 2001). Our results are a contribution to the literature on optimal waste and recycling policy in a world where producers can choose product design. As with many previous studies, we find merit in a combined output tax/recycling subsidy—i.e., a deposit–refund. But unlike some previous studies, we do not find that the deposit–refund is an alternative to a disposal fee. Rather, both instruments appear to be necessary to fully implement the constrained optimal level of waste, recycling, and environmental design.

Appendix A. Derivation of Eq. (9) R The social planner maximizes R consumer R utility, Vð qðuÞdu; WÞ s.t. the aggregate material balance condition that vðuÞdu ¼ V1 qðuÞdu ¼ W and the non-material resource constraint: Z Z Z Z qðuÞdu þ ðkðrÞ þ T2 Þ qðuÞdu þ ðkðrðuÞÞ R ¼ m þ g E vðuÞdu þ g D þ T2 þ T3 ÞqðuÞdu þ

Z

V1

V2

V3

cðrðuÞ; qðuÞ; uÞdu;

where V1 , V2 and V3 are the sets of products which are destined for landfills, curbside recycling and recycling with payment, respectively. This resource constraint states that the total use of non-material goods must be no greater than the total endowment, R. We linearize the objective20 around the efficient allocation to obtain R Vq qðuÞdu þ VW W þ m, plus a constant, then substitute in the constraints and collect terms, to generate the following objective: Z Z Z Vq qðuÞdu  cðrðuÞ; qðuÞ; uÞdu  ðg D þ g E  VW Þ qðuÞdu  ðkðrÞ þ T2 Þ

Z V2

qðuÞdu 

Z

V1

qðuÞðkðrðuÞÞ þ T2 þ T3 Þdu:

V3

We use the definition of SMC in Eq. (10) to collect terms, and the result is Eq. (9). 20 We take this approach so that we can directly compare the social planner’s objective function with the private profit function, Eq. (7), and identify the tax and subsidies that will make the two expressions coincide. The objective functions are not differentiable w.r.t. some of the choice variables, thus we cannot use the standard approach of fully linearizing by taking first order conditions.

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303

Appendix B. The social planner’s choice of r and r¯ Let firms be ordered by constrained optimal recyclability, so that u < u are not accepted by recyclers, u between u and u¯ are suitable for curbside collection and those over u¯ are suitable for recycling with payment. Consider the following problem21: Zu max

ðV¯ q q1 ðuÞ  q1 ðuÞðg E þ g D  VW Þ  cð0; q1 ðuÞ; uÞÞdu

0

þ

Z

u¯

ðV¯ q q2 ðuÞ  q2 ðuÞðkðrÞ þ T2 Þ  cðr; q2 ðuÞ; uÞÞdu

u

þ

Z

u¯

1

ðVq q3 ðuÞ  q3 ðuÞðkðrðuÞÞ þ T2 þ T3 Þ  cðrðuÞ; q3 ðuÞ; uÞÞdu:

The FOCs w.r.t. u, u¯ and r imply the following: cð0; q1 ðuÞ; uÞ cðrðuÞ; q2 ðuÞ; uÞ þ ðg E þ g D  VW Þ ¼ þ kðrÞ þ T2 ; q1 ðuÞ q2 ðuÞ

(B.1)

¯ uÞ ¯ ¯ q3 ðuÞ; ¯ uÞ ¯ cðr; q2 ðuÞ; cðrðuÞ; ¯ þ T3 ; þ kðrÞ ¼ þ kðrðuÞÞ q3 ðuÞ q2 ðuÞ

(B.2)

Z

u¯

ðcr ðr; q2 ðuÞ; uÞ þ q2 ðuÞðkr ðrÞ þ T2 ÞÞdu ¼ 0:

(B.3)

u

The constrained optimal choice of r is characterized in (B.3). However, the optimal choice of r¯ is not unique. Recall that r¯ is the level of recyclability at which consumers are indifferent about which form of recycling to choose. As explained above, no producer will design a product to have r strictly between r and r, ¯ as a reduction in recyclability will save costs but not reduce revenue. So the optimal level for r¯ can be any value between r and the lowest value of ¯ r, above r, that might be (constrained) efficient for a producer to design—i.e., rðuÞ. It remains to be shown that the value of r¯ that follows from (14) to (B.3) really will fall in ¯ We only need to confirm that r¯  rðuÞ, ¯ i.e., that a consumer would the interval from r to rðuÞ. ¯ sell a used product with r ¼ rðuÞ rather than leave it at the curb. To see this, recall that average ¯ q3 ðuÞ; ¯ uÞ=q ¯ 3 ðuÞ ¯ > cðr; q2 ðuÞ; ¯ uÞ=q ¯ 2 ðuÞ. ¯ But costs are increasing in recyclability, so cðrðuÞ; then Eq. (B.2) has the following implication: ¯ þ T3 : kðrÞ > kðr
ðuÞÞ

(B.4)

Next, recall that if SMC ¼ PMC, then the difference in material costs from r ¼ r to r  r¯ is (B.5) kðrÞ þ T3  kðrÞ ¼ T3  pr þ ðt3  t2 Þ: 21 ¯ q1 ðuÞ, q2 ðuÞ and Social costs of removal are equivalent for two different methods, when a firm is at u or u. q3 ðuÞ are the levels of output for u when r is 0, r and over r¯ respectively.

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We know from (B.4) that the LHS is negative. Therefore, the RHS will be too. But we also ¯ > T3 , and so a consumer would wish know that t2 ¼ t3 ¼ kðrÞ  g E . Therefore, pr ðrðuÞÞ
¯ to take a product with r ¼ r ðuÞ to a reverse vending machine.

Appendix C. Derivation of the policy settings under incomplete sorting Reconciliation of PMC with SMC requires (i) t1 þ f ¼ g D  VW , (ii) pðrÞðkðrÞ  g E Þ t2 ¼ ð1  pðrÞÞð f  ðg D  VW ÞÞ, and (iii) pðrÞðt3  s3 Þ ¼ ð1  pðrÞÞððg D  VW Þ ð f þ t3 ÞÞ; 8 r  r. ¯ Efficient recycling decisions (with minimizing PRC equivalent to minimizing SRC as reported in Tables 3 and 4) requires (iv) f ¼ ðg D  VW Þ  ðkðrÞ  g E Þ and (v) g D  VW ¼ f þ s3 . Combining (iii) and (v) reveals that t3 ¼ s3 , and so f þ T3 ¼ g D  VW . But then (iv) implies that t3 ¼ s3 ¼ kðrÞ  g E . Combining (ii) and (iv) reveals that t2 ¼ kðrÞ  g E , which we know is equal to s2 . Combining (i) and (iv) reveals that t1 is also equal to kðrÞ  g E . The conclusion is as reported in Section 5. We know that f ¼ ðg D  VW Þ  ðkðrÞ  g E Þ. But given that average costs are increasing in recyclability, Eq. (B.1) implies that g D  VW > kðrÞ  g E . Consequently, the disposal fee will be positive. Now imagine that manufacturers keep unclaimed deposits. Then (iii) is amended to pðrÞðt3  s3 Þ ¼ ð1  pðrÞÞðg D  VW  f Þ; 8 r  r. ¯ As a result, we need t3 ¼ ðkðrÞ  g E Þ=pðrÞ; 8 r > r. ¯ But this is impossible if p0 ðrÞ > 0.

Appendix D. Multiple types of material input Let there be j ¼ 1; . . . ; J different materials. Let b j ðuÞ ¼ v j ðuÞ þ r j ðuÞ be the amount of material j used in product u. Now producer u maximizes the following generalization of Eq. (7): V¯ q qðuÞ  qðuÞPMCðrðuÞ; b1 ðuÞ; . . . ; bJ ðuÞÞ  cðrðuÞ; b1 ðuÞ; . . . ; bJ ðuÞ; qðuÞ; uÞ; P subject to the constraint that j b j ðuÞ ¼ qðuÞ. The social planner’s objective is also amended: V¯ q qðuÞ  qðuÞSMCðrðuÞ; b1 ðuÞ; . . . ; bJ ðuÞÞ  cðrðuÞ; b1 ðuÞ; . . . ; bJ ðuÞ; qðuÞ; uÞ: P j Recyclability is represented by the value of the function j g E b j ðuÞ kðrðuÞ; b1 ðuÞ; . . . ; bJ ðuÞÞ. The analog to r of Section 3 is now a value of this function, say g. The constrained social optimum can be attained if t ¼ s ¼ g and f ¼ g D  VW þ g.

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