The recovery of products and materials for reuse: The global context of resource management

Resources, Conservation & Recycling 145 (2019) 422–447

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The recovery of products and materials for reuse: The global context of resource management

T

Faye Duchina, , Stephen H. Levineb ⁎

a b

Department of Economics, Rensselaer Polytechnic Institute, Troy, NY, USA Department of Civil and Environmental Engineering, Tufts University, Medford, MA, USA

ARTICLE INFO

ABSTRACT

Keywords: Global resource management Economics-engineering collaboration Recycling impacts on comparative advantage World Trade Model (WTM) Rectangular Choice-of-Technology (RCOT) model

We propose a framework for evaluating alternative approaches for recovering products and materials from capital goods that are no longer in use. It calls for deepening the existing collaborations between input-output economists and industrial ecologists to develop scenarios for the future and databases to support the analysis of global strategies for resource management. Our formulation offers the endogenous choice among technologies subject to resource constraints to minimize economy-wide use of factors of production in satisfying final demand. The determination is made on the basis of comparative advantage for a single economy and for the global setting. We develop an illustrative database for three regions characterized by different resource profiles for natural resource endowments and for the accumulation of built capital; they are roughly modeled on Japan, Guinea, and India. The material and economic consequences for each region, and for the world as a whole, are then calculated under alternative recovery scenarios. Sharp contrasts in region-specific outcomes are evident, and clear impacts of actions in one region on outcomes in other regions demonstrate the need for a global context. Next steps include making dynamics explicit by incorporating lifetimes of durable goods and infrastructure, varying production duration periods, and resource stock-flow relationships. The final section addresses the corresponding development challenges, in particular those surrounding jobs and livelihoods. These concerns need to inform design priorities for the scale and degree of decentralization of future technological systems, which are readily represented as technological alternatives.

“The closed economy of the future might … be called the “spaceman” economy, in which the earth has become a single spaceship without unlimited reservoirs of anything, either for extraction or for pollution.” Kenneth Boulding (1966) 1. Introduction The model-based literature on resource management, including studies of waste processing, generally takes a national perspective. This focus reflects the concerns about future access and rising prices on the part of countries that depend on imports for vital resources. Growing interest in recovery of resources from abandoned capital goods and infrastructure can substantially enhance resource security in countries reliant on resource imports while also generating employment and lowering costs. However, countries face very different impacts from an increasingly steeper global rate of recovery of resources, and the decisions taken by some actors will have strong repercussions throughout ⁎

the global economic system. One case is that of rich, industrialized economies with a great deal of built capital and only meager material resources, for which they depend on imports, for example Japan. Another case includes poor countries with little accumulation of built capital for product or material recovery but abundant resource endowments: an example is Guinea, which is dependent on metal exports for most of its foreign exchange. If a fully circular, global economy were achieved, these resource exports could disappear, an economic disaster for countries dependent on this source of foreign exchange. However, expanding imports of resources by countries with large and growing economies, such as India and China, could offset if not exceed the material savings. The objective of this paper is to propose an analytic framework for gaining insight into prospective crises in the global resource economy as a basis for designing cooperative strategies and governance institutions. While we cannot expect to predict how this complex situation will evolve, central issues include the quantities and geographic distribution of physical endowments of resources, technologies and systems of technologies related to the extraction, use, and

Corresponding author. E-mail address: [email protected] (F. Duchin).

https://doi.org/10.1016/j.resconrec.2018.10.028 Received 24 April 2018; Received in revised form 19 October 2018; Accepted 23 October 2018 Available online 27 March 2019 0921-3449/ © 2018 Elsevier B.V. All rights reserved.

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recovery of resources, and key features of individual economies and the global economic system such as protectionism and property rights to resources. The field of industrial ecology is engaged with many aspects of both technological innovation and material recovery, combining approaches originating in life-cycle assessment (LCA) and material flow analysis (MFA). Input-output economics (IOE) provides the conceptual link between LCA, concerned with production processes, and MFA, which describes stocks and flows of the resources used in production. IOE provides the model logic for associating technologies with production requirements including resources, sectoral interdependence, and consumer demand as well as assuring economy-wide coverage for structuring the corresponding databases. The important recent innovation of waste input-output analysis (WIO) (Nakamura and Kondo, 2002) integrates these three areas in a conceptual framework for evaluating the efficacy of alternative solution approaches. WIO analysis contributes the pioneering detailed databases of wastes and waste-processing technologies for Japan. In addition, several global input-output databases are now available (Owen, 2017), including a recent global waste database that is compatible with input-output sector-level classifications (Tisserant et al., 2017). The first objective of this paper is to make use of the WIO capability to explore options for resource strategies and their likely implications for a single economy using the Rectangular Choice-of-Technology (RCOT) model (Duchin and Levine, 2011). The mathematical representation will treat structures or products that are no longer valued by their owners as potentially recoverable by any number of technologies that make use of them in various ways. We use RCOT, a linear programming model, to examine and evaluate options to manage obsolete goods or structures in each of the three types of regions described above. The options include longer product lifetimes, product remanufacturing for reuse, recovery of metals from obsolete products or structures, and landfilling of wastes. The evaluation is based on minimizing the total use of factors of production, each weighted by its ex ante price. The second objective is to broaden the scope by allowing the regions to trade with each other according to their comparative advantages. We analyze simplified versions of three of the scenarios for the three-region world economy by incorporating the RCOT model into the World Trade Model (WTM) (Duchin, 2005; Duchin and Levine, 2012). The latter framework allows us to compare the implications of the same strategy when a single economy is analyzed and when the same scenario situates the region within a global economy. The solution algorithm for the WIO model allows for a choice among alternative waste management technologies while also retaining their individual identities. However, the wastes are distributed to the technologies according to exogenous assumptions in order to allow it, like the multi-regional input-output (MRIO) model, to capture intersectoral and in the latter case inter-regional interdependence, by inverting a square matrix. Using inter-industry matrices that are rectangular, RCOT and the WTM represent an input-output representation of an economy with endogenous technological choices as a linear program that allows for the intimate interaction between physical variables and costs and prices. Our usual choice criterion is to minimize the economywide quantity of factor inputs, each weighted by its ex ante price, needed to satisfy given final demand. The fundamental innovation in our linear program formulation is to treat limited resource endowments of land, water, metals, and other minerals as factors of production along with labor and built capital, and to impose constraints on their availability for use in production. Imposing these constraints allows these models to reflect the most fundamentally integrative concept of

economics, the theory of exchange based on comparative advantage; this theory provides the default logic for the models, except under scenarios where it is overridden by other assumptions such as government regulations. It is the ability to represent and explain these relations according to a transparent, well-defined logic that makes it possible to extend the analysis of MRIO databases about the past to evaluating scenarios for the future (see Duchin et al., 2016; Duchin and Levine, 2016). The remainder of the paper is structured as follows. Section 2 reviews part of the substantial literature on waste processing as well as publications describing the model and empirical applications of the Waste Input-Output and of the Rectangular Choice-of-Technology and World Trade Model formulations. Section 3 analyzes six resource management scenarios for the three regions and discusses the outcomes. Section 4 reports on the much smaller, more conceptual and less technical, literature that situates the analysis of resource management options within a global framework. It includes the analysis of three scenarios using the WTM/RCOT model and compares the no-trade and world-model results, demonstrating why results based on one-region analysis can lead to misleading conclusions. Section 5 provides a summary and describes the models’ strengths, limitations, and next steps. It also discusses data requirements and concepts for global scenarios. The paper includes four Appendices. Appendix A describes the sectors, technologies, factors of production, wastes, and conversion factors that figure in the scenarios. Appendix B shows the values of technical coefficients and exogenous variables and scenario outcomes for the one-region analysis of six scenarios, and Appendix C does the same for the no-trade and global comparisons under three scenarios analyzed using the WTM/RCOT. Finally, Appendix D discusses the relationship between shadow prices, an endogenous variable in all linear programs, and the economic scarcity rent, which is a vital component of our price analysis. The shadow price measures the reduction in overall factor costs if one more unit of a scarce resource were made available. In RCOT the shadow price is generally is equal to our scarcity rent. However, the present article introduces imposition of a regulation that may increase factor use. In this case, as we shall show, the rent may exceed the shadow price. 2. Review of the literature 2.1. Managing resources The “circular economy” closes the loops involving the extraction of raw materials, their utilization in the production and use of structures and goods, and their disposition at the end of their useful lifetimes by recycling materials and products multiple times (Geissdoerfer et al., 2017). The concept of the circular economy has been around for several decades (Pearce and Turner, 1989), and the general idea dates back at least to the 1960s (Boulding, 1966). Starting in the 1970s it was widely recognized that waste is not homogeneous but rather consists of multiple components amenable to a variety of management strategies (Schall, 1992). Early efforts to manage wastes are the European Union’s Council Directive (1975) and the Resource Conservation and Recovery Act of 1976 in the United States (Kovacs and Klucsik, 1977). A waste management hierarchy was first articulated in 1979 in the Netherlands (described by Kemp, 2007). Numerous versions have followed, including that of Graedel and Allenby (1995), who introduced it to Industrial Ecology as the Product Recycling Preference Hierarchy. China’s law setting out conditions for a circular economy came into force in 2009 and is the first legal act of its

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kind (Circular Economy Promotion Law, 2018).

The RCOT primal and dual models for n sectors, t technologies, and k factors take the following form:

2.2. The waste input-output (WIO) model

Primal

Wassily Leontief, the creator of input-output economics, also developed the first input-output framework for quantifying the generation of pollutants and their treatment (Leontief, 1970). (Nakamura and Kondo, 2002, 2009) substantially augment that basic model by developing a detailed representation of the interactions of waste management activities with sectors producing other goods and services. Their empirical studies include the evaluation of alternative life-cycle strategies (Kondo and Nakamura, 2004), of the fates of metals and scrap (e.g., Nakamura et al., 2007), and the costs of recycling home appliances (Nakamura and Kondo, 2006). Nakamura et al. (2009) examine options for handling polyvinyl chloride in Japan, and Takase et al. (2005) look at prospects for sustainable consumption in Japan. Nakamura et al. (2014) develop the MaTrace model for tracking materials over any number of life cycles stages including recovery cycles. Nakamura et al. (2017) and Pauliuk et al. (2017) apply this model for the case of steel, the latter in a global context. Kondo and Nakamura (2005) have situated the WIO model in a linear programming formulation (see the next section) that allows the endogenous choice among alternative recovery strategies; it was recently applied to optimize recovery of steel scrap from end-of-life vehicles in Japan (Ohno et al., 2017). These and other empirical WIO studies develop databases with a depth of technological detail that is characteristic of LCA studies but unprecedented in input-output analyses. The further development of these databases will be indispensable for realizing the kind of agenda described below.

Dual T

Min Z = π F*x* Max W = pTy−rTf subject to: subject to: (I*−A*)x* ≥ y (I*−A*)Tp ≤ F*T(π + r) F*x* ≤ f x* ≥ 0 p ≥ 0. Matrices of parameters I* sector-technology associations (n x t) A* intermediate requirements per unit of output (n x t) F* factor requirements per unit of output (k x t) Exogenous variables y final demand (consumption) (n x 1) f factor endowments (k x 1) π ex ante factor prices (k x 1) Endogenous variables x* output by technology (t x 1) p prices by sector (n x1) r factor scarcity rents (k x 1)

The asterisk superscript (*) for a matrix (or vector) indicates that its columns (or components) correspond to individual technologies. I* is the rectangular generalization of the square identity matrix I that places, in the row for a given sector, 1 s in the columns for all technologies available to that sector and 0 s elsewhere in the row. In the primal, total factor use, weighted by constant prices, is calculated as the scalar quantity Z = πTF*x*. The dual (which follows directly from the formulation of the primal) solves for the values of p and r that maximize the value of final demand net of factor rents, W = pTy - rTf. Factors that are fully utilized earn a scarcity rent, r, in addition to the ex ante price π. Note that in the present context, r may be positive or negative; see the discussion below and in Appendix D. Taking scarcity rents into account, the total factor costs are pTy = (π + r)TF*x*. This relationship holds because, according to the duality principle of linear programming, at the optimal solution Z = W. The RCOT model can represent recovery of goods and materials and disposition of waste, along with the variety of other sectors comprising an economy. For this application RCOT broadens the relation between alternative technologies available to a sector. Thus, mining of virgin metals and recovery of metal from discarded products are alternative technologies for producing metals, although they would not belong to similar sectors as conventionally defined. The need to customize the model for the current applications is limited to the handling of data. We make endogenous several categories of data that are usually treated as exogenous in input-output models. This endogeneity reflects the fact that recovery of wastes for reuse increases the interconnectedness of the economy. It is described in the next section after the brief presentation of the WTM/RCOT model.

2.3. The rectangular choice-of-technology model (RCOT) This paper employs the Rectangular Choice-of-Technology (RCOT) model (Duchin and Levine, 2011) to represent the availability and use of resources, options for their management, and associated costs and prices. Interpretation of model results exploits the consistency and interdependency between the primal model and the price dual, and factor prices (e.g., wage rates and unit prices of resources) are conceptualized as the sum of two components, an exogenous unit price that is specified by the scenario and the all-important rents that are positive for resources that become physically scarce. When two or more technologies for producing a given product are simultaneously in use, it is generally the highest-cost technology (of those which are active) that sets the price. Lower-cost producers earn a scarcity rent, amounting to the difference between the established price and their own costs of production. Resource endowments are typically absent from input-output models, including the WIO model as well as WIO-LP, its linear programming version. It is by explicitly limiting resource use to available endowments that the RCOT model is able not only to quantify economic rents on scarce resources but also to structurally incorporate the stockflow relations of MFA with LCA within the economic analysis. While a column of technical coefficients is needed to represent each technology available to a sector, the sector’s deliveries are shown in a single row. That set of production options is selected that minimizes factor use for the system as a whole in satisfying demand, subject to factor availability and any other constraints such as government policies. Strømman et al. (2009) quantify results for trade-offs among alternative objective functions. The RCOT model has been incorporated into the World Trade Model (WTM) (Duchin, 2005), to allow for regionlevel choices among technologies as well as for specialization among world regions (Duchin and Levine, 2012).

2.4. The world trade model (WTM) The World Trade Model (WTM) follows the same economic logic as the RCOT model but extends production choices from different technologies in one region to also allow the choice among regions. Empirical applications of this model include analyses of resource use and recovery in the context of the global economy (Springer and Duchin, 2014; Cazcarro et al., 2016) and several studies of water use for agriculture within individual regions of the Mexican economy (LopezMorales and Duchin, 2011 and 2015; Duchin and Lopez-Morales,

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2012). The WTM/RCOT primal and dual models for m regions, n sectors, t technologies, and k factors are shown below: the matrices and vectors are defined as for the RCOT model (above) except that now they are also distinguished by a region-specific subscript, except for prices of inter-regionally traded goods and services, p, which are assumed to have a world price:

effectively making it endogenous with consumers covering the costs. The number of waste computers is f3 - (f*3,1.2 x*1.2) - x*2.2, where the second term is the number of used computers from which physically incorporated metal is recovered, and the third term is the number of used computers that are remanufactured. (See Appendix A for the notation of individual parameters: f3 is the endowment of the third factor, f*3,1.2 is the component of F* quantifying the input of the third factor to the first sector for its second technological option, and x*i.j is the output of the ith sector using its jth technology.) Let v0 be the volume of a waste computer; then the required volume of landfilling (in cubic meters) is given by: y4 = v0[f3 − (f*3,1.2 x*1.2) − x*2.2] Both final demand for computers, y2, and the stock of used computers, f3, are specified exogenously for each scenario. Our illustrative data make it more economical to remanufacture a used computer than to recover its embodied metal, provided that there is adequate demand for computers to absorb all the remanufactured ones. In these computations, remanufactured computers are considered to be homogeneous with new ones; explicit representation of imperfect substitutes is discussed in the last section of the paper. Let g be the number of used computers required by the metal recovery technology to yield one kg of metal; then f*3,1.2 = g, where used computers are the third factor, sector 1 produces metals, and metal recovery is its second technological option. The production of computers is the second sector, remanufacturing used computers is its second technological choice, and it takes exactly one used computer to generate one remanufactured computer; consequently, f*3,2.2 = 1. Both recycling technologies generate residue that must be landfilled. Let the volumes of residue from a used computer be v1 (m3/unit) for metal recovery and v2 per remanufactured computer (m3/unit). Then a*4,1.2 = v1 * g = v1 (f*3,1.2) is the requirement for landfill services (the fourth sector) in m3/kg of metal produced by the metal recovery technology, where the volume of residue determines the volume of land required to landfill it. Likewise, a*4,2.2 = v2 is the amount of landfill service required for residue per computer remanufactured. For scenarios where one or both recovery options are not operative (the case for A0 through A3, for example), we constrain the corresponding component of x* to equal 0. The values for g and v0, v1, and v2 are given in Appendix A. Appendix B contains the input-output data for the first set of calculations, scenarios A0 to A5. The sectors and technologies are intended to represent realistic options, albeit in a highly simplified way. The data are intended to be realistic as a stylized representation of each economy. We point out several assumptions built in to the data. We assure that remanufacture of used computers would be less costly than manufacture of new computers and a more cost-effective use of discarded computers than recovery of metal from them. The data assumptions for the two metal-producing technologies lie behind the complex relation between them. One explicit intention was that the region with comparative advantage in mining ore would find that option less costly than recovering metal in the absence of additional constraints: this subject is discussed in detail below. Finally, we assume for simplicity that the useful lifetime of a product can be extended by the decision of the consumer without changes to its production inputs, which is often but not always the case (see Kondo and Nakamura, 2004; Allwood et al., 2011). Note that any other sets of assumptions represented in the illustrative database could be explored. For an empirical analysis, the data values would naturally be based on technical data developed independently of any such a priori assumptions.

Next we formulate a set of alternative scenarios for resource management to demonstrate the use of this framework in a single region and develop an illustrative database to demonstrate the capabilities of the model. 3. Managing resources in a single region 3.1. Scenarios and data The first analysis involves six scenarios about resource management options for an economy, and we evaluate them for the three regions described earlier, highly stylized representations of Japan, Guinea, and India. The scenarios assume four sectors producing metals, computers, other machines, and landfilling of wastes. There are six technologies, as metal may be produced by mining virgin ores or recovery from used computers, while computers may be newly produced or remanufactured from used computers. The four factors of production are labor, ore, used computers, and land; and there are two kinds of wastes, the residues from recovery technologies and those used computers that are not recycled but destined for landfill. The sectors, technologies, factors, and wastes are described in Appendix A. Scenarios A0 through A5 prescribe alternative ways of dealing with the used computers. A0, with no recovery of used computers and no landfilling, serves as the baseline: any unwanted used computers are disposed of informally, without cost. All subsequent scenarios incur costs associated with the requirement that used computers that are not recovered are disposed of in landfills. Analytically, this treatment serves to impose a government regulation to over-ride the objective of minimized factor use (discussed below). A1 offers no recovery options; consequently all used computers must be landfilled. A2 allows only for metal recovery from used computers, A3 allows only for remanufacture of used computers, and A4 offers both recovery options. A5 also offers both recovery options and in addition assumes that computers have a useful lifetime double that under the other scenarios. Appendix B shows the scenario assumptions and the databases for each of the regions under all scenarios. 3.2. The database The illustrative database developed for the three regions aims to capture, albeit in a simple and stylized way, the differences among the three kinds of regions most relevant to this inquiry. While A*, F*, and y are usually exogenous in an input-output database, there are several exceptions in the present application. Landfilling wastes is represented as final demand for that service,

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consumers disposing of used computers assuming the cost. Total factor use is lower under A2 than A1 because there is cost saving from the recovery of metal. However, both sources of metals must operate simultaneously since the quantity of metal recovered cannot fully satisfy demand. Metal recovery from used computers avoids the need to landfill the used computers, and this saving would enhance any cost advantage (or offset any cost disadvantage) relative to virgin metals. With consumers again charged the cost that would be incurred if their used computers were landfilled, the recovery of metal from each used computer retains a net positive rent. If the net rent were negative despite the avoidance of landfilling the used computers, then recycling of used computers for metal recovery would not be economically viable unless subsidized by additional sources, for example the municipal government. This representation of the combination of economy-wide cost-minimization with environmental regulation opens up a new avenue for analytic exploration: an end-of-life item may be either an economic asset or burden, and the concept of a rent is substantially broadened. We return to this subject in the closing sections of the paper and in Appendix D. Scenario A3 offers remanufacturing UCs as the sole recovery option, and the solution is the same as that for A4 since remanufacturing turns out to be more economic than recovering metal. It is considerably less costly than production of new computers, and all the UCs are remanufactured. A consequence is the large drop (about 20%) in total factor use, including in labor. However, factor earnings increase in all regions by about 10% due to the emergence of rents on used computers. UCs are unambiguously a valuable asset under this scenario, and total income (including the rents) is even higher than under A0, which imposed no requirement to dispose of used computers responsibly. The rents could be paid to those providing UCs, retained as income for the remanufacturing firm, or appropriated by governments as a tax that would be used to subsidize costly options that are imposed but are not

Fig. 1. Total Factor Use (TFU) and Total Factor Earnings (TFE) under Scenarios A0 through A5. Note: Factor use is measured at constant prices while factor earnings include scarcity rents.

3.3. Scenario results Scenario A0, with no recovery and no landfilling of used computers (UC) establishes a baseline for costs and prices, production, jobs and resource use, and factor incomes. Summary results for the three regions jointly include money costs (of factor inputs) in both constant prices and including rents in Fig. 1, outputs by technology in Fig. 2, and factor use in physical units in Fig. 3. The tables in Appendix B provide more detailed results for the individual regions. The landfilling requirement under scenario A1 increases costs over the baseline values in proportion to the number of UCs in each region, but it makes sure they are not dumped in the landscape and it generates jobs and incomes. Landfilling is represented as final demand, with the

Fig. 2. Output by Technology under Scenarios A0 through A5. 426

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Fig. 3. Factor Use under Scenarios A0 through A5.

cost-effective. However, the high efficiency of this outcome results in a substantial reduction in jobs, an important topic to which we return. Finally we calculate outcomes for A5, a version of A4 that assumes that consumers retain the average computer for a much longer lifetime. This is represented by a lower availability of UCs and also lower intermediate and final demand for computers. One premise behind deep recovery of resources is that it is desirable to lower factor use for delivering final goods, and that is the outcome here for remanufacture of used computers and longer lifetimes. However, they are not surprisingly accompanied by very substantial reductions in jobs. We return to this subject in the final section of the paper.

energy, or climate,” they anticipate the need for “extensive technological transformations and governmental initiatives,” for examining multiple resources and resource uses simultaneously, and for taking explicit account of geological constraints (p. 4), meaning factor endowments. Korhonen et al. (2018) point out that most studies of resource management are intended to support policymakers and business advocacy bodies and focus almost exclusively on physical flows and metrics, tools, and computations. They fault this literature for failing to address the need for changes in underlying values, societal structures, and world views. Exner et al. (2015) express concerns about economic as well as climatic instability, geological constraints, and the uneven geography of both geologic resources and socioeconomic attributes. Citing many of the same sources as the more technical paper of Elshkaki et al. (2018), they argue that even with complete recovery of metals in use, countries that are today not already industrialized would be unable to put in place adequate built capital to support development due to geological resource constraints. The authors judge that these very real physical limits are not yet sufficiently recognized and studied and conclude that the latter countries need “a raw materials policy that conserves as much internal resources [as needed over the long term] for the construction of important infrastructure” rather than, say, allowing the near totality of their resources to be exported to other countries. Barteková and Kemp (2016) define the nature of the challenges as

4. Resource management in the global context 4.1. Review of the literature While almost all quantitative analyses of waste management strategies focus on an individual economy at one point in time, several authors make a compelling case that the context for resource strategy in the 21st century must be global and future-oriented. Elshkaki et al. (2018) evaluate the likely mid-century situation for seven major metals. They anticipate that demand will increase 21–37 times, with metal recycling likely able to satisfy only a modest 15% of demand. Arguing that the futures of key metals are “as important as those of water,

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“tackling supply risk,” so different world regions clearly need different resource strategies depending on whether they are rich or poor in built capital and in geologic resources. The authors describe China’s equity positions in foreign mining companies and grants and loans given in exchange for future assured access to resources. Japan also secures resources through public-private partnerships and long-term agreements for access, as well as involvement with seabed exploration and ocean industries. Their discussions of strategies cover only the countries the authors identify as the five major global stakeholders: China, the US, Europe, Japan and Australia. McDowall et al. (2017) review newspapers from China and from six European countries to discern differences in approaches to dealing with resource supply risk and the circular economy. China’s focus is on production choices and land-use planning for substantial further urbanization, while European countries wish to promote changes in consumption and are equally concerned about reducing business costs to improve global competitiveness. The authors conclude that both China and European countries perceive the need for a “new model reconciling economic and environmental imperatives” (p. 3). Kojima (2017) describes remanufacturing as a promising global industry in its early stages, with its expansion constrained by trade regulations. Some of the regulations are intentional, like concerns in developing countries to keep out imports of low quality or outright wastes or to protect emerging domestic industries from competition. However, other constraints are unintentional and reflect misunderstandings like failing to systematically distinguish wastes from secondhand goods, or from remanufactured components and end products. Lee et al. (2017) point out the advantages of the growth of this global sector in savings of material resources and energy, job creation in what is intrinsically a labor-intensive sector, and price stabilization by holding costs down. They describe the current practices in eight countries plus the European Union and call for an invigorated practice of upfront design for subsequent disassembly. Like Kojima, they find the prospects very promising and call for global cooperation in designing institutional strategies.

scenarios are simplified relative to those of Section 3: here we omit obligatory landfilling to make the logic behind outcomes more transparent in that compulsory land-filling introduces a complex impact on rents (discussed in Sections 3.3 and 5.2). W0 is a baseline scenario with no recycling options (corresponding to A0 of Section 3), W1 provides access to metal recovery from used computers (it corresponds to A2 but without mandatory landfilling of used computers or of recovery residues), and under W2 both metal recovery and remanufacturing of used computers are available options (corresponding to A4 but without mandatory landfilling). Each scenario is run both as a no-trade computation (RCOT for one region) and also allowing trade (WTM/RCOT). (The no-trade versions of scenarios W1, W2, and W3 are similar to A0, A2, and A4, respectively, but in the absence of landfilling requirements.) The data and assumptions for these scenarios and the scenario results for the individual regions are shown in Appendix C and summarized for the three-region world in Figs. 4–6. While each region must operate all sectors in the no-trade version of the baseline scenario (W0), the WTM version shows a distinct pattern of specialization with region 1 producing only computers, fully exhausting its supply of labor; region 2 specializing in mining ore, fully utilizing both its labor supply and its ore; and region 3 as the only producer of other machines. Regions 1 and 2 cannot satisfy total global demand for computers and metal, so higher-cost region 3 must supplement their outputs, setting the world price for all three traded products. As a consequence, regions 1 and 2 earn substantial scarcity rents as lowercost producers. Region 2, the poor but resource-rich developing country, experiences a dramatic increase in employment and in income relative to its no-trade outcome by fully exploiting its low-cost resource to satisfy global demand. Trade, however, is not beneficial for region 3, which now incurs a huge trade deficit, as lower-cost imports substitute for its domestic production. Global trade economizes on factors, and now regions 1 and 2 are able to satisfy all demand for most products at lower cost. For all regions combined, total factor use falls but total income is maintained, essentially in the form of large resource rents in region 2 (Fig. 4). This dramatic redistribution of global income to region 2 parallels the economic boom in the Middle East in the 20th century associated with global exports of petroleum. Scenario W1 allows for the recovery of metal from used computers. In the absence of any requirement to landfill the non-metallic residue (or the waste computers), this is less costly than the alternative in regions 1 and 3. In region 2 mining ore is less costly so there is no recovery of metal in this region, and the outcomes change very little relative to W0. In the presence of trade, however, region 2 uses its full

4.2. Scenario analysis with inter-regional trade The last few paragraphs make clear the centrality of trade of processed resources and embodied resources, and changes in trade patterns, to the global resource economy. In our second set of scenarios, we next treat the three regions as comprising a global economy by allowing them to trade on the basis of their comparative advantages. The

Fig. 4. Total Factor Use (TFU) and Total Factor Earnings (TFE) under Scenarios W0 through W2 (no trade on left, with trade on right). Note: Factor use measured at constant prices while factor earnings include scarcity rents.

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Fig. 5. Output by Technology under Scenarios W0 through W2 (no trade on left, with trade on right).

labor force to exploit all its virgin ore and exports almost all of it. Because world demand exceeds the amount region 2 can extract, region 3 recovers some metal from used computers, boosting the world price of metal. While globally the scenario is factor saving, with total jobs cut practically in half, region 2 benefits from a substantial increase in jobs and in income, especially income of labor and also for its ore, due to scarcity rents. Scenario W2 allows in addition for remanufacture of used computers, a more economic use of them than recovering embodied metal. All used computers are remanufactured, supplemented by the production of some new ones. Consequently, the price of computers does not change and remanufacturing enjoys substantial rents. Total factor use, and employment in particular, falls from W0 and W1 levels in all regions except region 2. Especially in the presence of trade, global employment and total factor use both fall substantially relative both to the no-trade W2 scenario and even to the W1 scenario with trade, as do

total earnings, which take scarcity rents into account. While factor use is not reduced much in region 2, its income falls by two-thirds because it is now able to supply total world demand for metal, eliminating its scarcity rent on ore. Nonetheless, the global distributions of income and of labor still shift sharply, both in the favor of region 2. Economies like region 3 are in the undesirable position of lacking both high-quality resource endowments as well as low-cost technologies for producing other tradable outputs. If a large economy like region 3 could establish sectors with significant comparative advantages based on lower costs, new technologies, or by exploiting unique domestic advantages, then the picture could change substantially. One outcome would be increased demand for metal, furnished by some combination of increased economic incentive for material recovery and exploitation of higher-cost deposits. However, steeper rates of recovery of metals and remanufacturing of used products using improved technologies that are more efficient and generate less residues, and production

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Fig. 6. Factor Use under Scenarios W0 through W2 (no trade on left, with trade on right).

technologies that provide the same functionality with substantially lower material requirements (e.g., nanomaterials), would operate in the other direction.

models offer endogenous choices among alternative technologies based on economic criteria and, for the WTM/RCOT, endogenous responses of trade flows and global income distribution to scenario assumptions based on the concept of comparative advantage. The paper illustrates the formulation of scenarios and the construction and manipulation of an illustrative database and interprets the outcome of scenarios allowing for remanufacturing of unwanted products and recovery of metals from them. We carry out the analysis for three types of economic regions and provide illustrative results for individual regions and the case where the regions trade among themselves. The results show the kinds of considerations behind potential advantages from trade and also the dramatic changes to which a trading region may be exposed due to actions taken in other regions. The models are concise and their logic is transparent, the scenarios are simple and the data are only illustrative. However, we feel that the results are sufficiently compelling to suggest the value of a full-scale empirical analysis with a well-documented database. The analysis requires technologically informed scenarios exploring resource strategies for different categories of economies and, importantly, for global cooperation and institution-building.

5. Discussion and next steps 5.1. Summary This paper analyzes alternative ways of addressing resource management challenges for individual regions and for regions that function as part of the world economy. The results reinforce the conviction that a global, future-oriented perspective is essential for understanding the nature of the challenges and formulating strategies to address them. The analyses are carried out using the Rectangular Choice-ofTechnology (RCOT) model for one region and its incorporation with the World Trade Model (WTM) for the global analysis. These models represent the generation, treatment, and disposal of unwanted but potentially valuable products using the same mathematical logic and notation that are applicable to other sectors of the economy. The 430

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A fundamental insight behind the theory of comparative advantage is that regions trade to exploit their differences in resource endowments, factor prices, and technologies. These exchanges create an interdependence that can lead to strong vulnerabilities in a given economy when there are disruptions in resource demand or supply, or technological innovations and shifts in policy, elsewhere in the global economy. Capturing these outcomes requires a multi-regional framework where strategic variables are responsive to scenario assumptions. The scenario outcomes illustrate the prospect for a poor but resource-rich country to export its resources for abundant current income and jobs and the situation of other countries dependent on access to these imports. While the former can lose these export markets and jobs when faced with extensive material recovery, those of the latter with abundant built capital can generate domestic employment through product remanufacture and material recycling. Long-term, co-operative strategies to reduce both countrylevel and global risks can be analyzed in this framework as scenarios. A new feature of this study is the combination in some scenarios of cost minimization and regulations, namely the obligatory landfilling of wastes. In the absence of trade and with no landfilling requirements, in the region with the global comparative advantage in mining virgin ore (region 2: see data for F* matrices in Appendix B, Table B.1), mining uses less factor input than recovery of used computers. By contrast, recovery of metal is less factor-intensive than mining in the other two regions. Consequently, all used computers are recovered with mining of virgin ore complementing the recovery of metal in these two regions. When landfilling requirements are imposed (scenario A2, see Appendix B, Table B.2.3), all used computers are recovered for metal in all regions, but this source of metal must in all three regions be supplemented by mining of virgin ore. Thus, under all scenarios in the absence of trade, whether or not landfilling requirements are imposed, the price of metal in each region is set by its cost of mining of virgin ore. In the presence of trade (scenario W1 with trade, Table C.2.2.2), however, the ore-rich region is able to exploit its comparative advantage in mining ore, exhausting its full supply. This metal production does not suffice to satisfy world demand, however, and region 3 not only recovers ore from all its used computers but also must mine some ore, the most factor-intensive of the three metal-producing activities, which therefore sets the world price. As a consequence, region 2 earns a large rent on its scarce ore.

rows as columns. However, different degrees of quality could be made explicit while maintaining the advantages of the RCOT model, with the representation depending on the specific attributes of the options. We offer some ideas on the assumption that the relative costs of production correlate with differential quality. Assuming that the new product has the highest cost of production with each remanufactured one earning a scarcity rent, the largest rent is earned by the least costly to produce, which is presumably also the one of lowest quality. A price rebate could be provided to purchasers of remanufactured computers in the amount of some portion of the rent, with the buyer’s choice of remanufactured product subject to assuring that total outlays of different consumers are constrained not to exceed their earnings (as is always the case for intermediate users). Such an implementation provides “closure” of the model for incomes and outlays. This closure is the focus of (Duchin, 1998), where it is implemented for different categories of households in Indonesia in the case of the basic, static, one-region inputoutput model. In a model closed for households, one could represent alternative consumption columns for different household categories and choose among them under an income constraint using the RCOT logic, which until now has been applied only to technological options subject to factor endowment constraints. 5.2.3. Dynamic input-output model Examining the implications of alternative longer-term strategies requires a dynamic perspective. Dynamics in the present context requires the introduction of four time-dependent phenomena. First, sectors desiring to expand their production capacity need to order capital goods on a time schedule in advance of their availability. Second, sectors producing capital goods or infrastructure need to schedule their own input requirements to meet client requirements. Third, the age of built capital in place needs to be tracked to assure it is maintained and replaced if it is not retired in advance of its useful life. Finally, changes in stocks of resources need to be reduced in each time period for flows utilized and augmented by new discoveries. We know of no dynamic model that incorporates all these features. Duchin and Szyld (1985) developed the first dynamic input-output model that was used for empirical analysis of scenarios for the future. First applied by Leontief and Duchin (1986), its fundamental innovation was to relax the unrealistic assumption that the existing capital stock needed to be fully utilized; this freed the solution from the “balanced growth path,” where the only feasible solution requires all sectors to grow, and furthermore to do so at the same rate. This dynamic input-output model features a primal model in mixed units and a dual price model that assures that income earned within an economy is available to cover not only consumption but also outlays for new investment. The dynamic economic model needs to be integrated within a global modeling framework that also represents changes in spatially situated resource stocks over time, the stock-flow relationships familiar in industrial ecology. Some of the challenges in realizing the required model are the needs first to conceptualize and then to compile a database that can satisfy these requirements. Input-output databases have traditionally been compiled from official censuses and surveys for past years; the figures are organized in a flow table measured in the domestic currency, with first-order consistency requiring that row totals (the money receipts from all deliveries made by a sector) equal column totals (the money payments for all sector inputs). Moving to mixed units – and especially moving from analysis of the past to evaluation of alternative scenarios for the future – shifts more of the burden for data compilation away from economists and accountants. Both the innovations and the data describing them depend on the expertise of engineers for system design and implementation and require their initiative in constructing the databases describing these prospects. WIO databases incorporate detailed technological information, contributed largely by engineers, and this kind of expertise is also needed for developing data needed for implementing dynamic models of the economy. The database developed for the dynamic model of Duchin and Szyld (1985) includes capital matrices that

5.2. Model strengths, limitations, next steps 5.2.1. Scarcity rents While RCOT and the WTM have been used in a number of empirical investigations, the present application makes use of some features for the first time. Discarded products, in the form of used computers in the numerical examples, are represented as factors of production, which are economic assets. However, when we impose the requirement that used goods that are not recovered need to be landfilled, which incurs costs, the choice between recovery vs. landfilling is endogenously determined based on a comparison of economic costs. This representation confers a unique status upon used goods: they are assets when the cost of recovery is lower than the cost of discarding them without any recovery, and burdens when recovery is more costly but is still considered in the public interest. In the current implementation, the cost saving, or the additional cost, is represented by an economic rent on used goods that may be positive, meaning recovery is cost-effective, or negative. See Appendix D for a more technical discussion. 5.2.2. Imperfect substitutes In the current implementation, a new computer and a remanufactured one, and virgin metals and recovered ones, are treated as “perfect substitutes,” which is sometimes but not always a reasonable approximation. One way to introduce distinctions in quality is to assign exogenous values for demand of new and recovered objects and represent the options in the standard way, namely by the same number of 431

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are very crudely estimated and very roughly estimated time lags for putting new capacity in place. The capital databases available today are still based on accounting data in money values and ex ante rates of depreciation with no physical counterparts. These data need to be expressed as columns of coefficients, not flows in money values and to include the representation as options of potential future innovations. Compiling much better data needs to be a priority objective. Levine and Romanoff (1989) initiated work along these lines decades ago and may provide a good base to build on.

may promote development in one economy while it undermines it in others. In the current information age when jobs are expected to be lost to information systems and robots, elimination of jobs is from a societal point of view seen as a negative rather than a positive outcome. Kondo and Nakamura (2004), for example, find in their empirical analysis that the extension of product life in Japan could achieve environmental objectives but also reduces input requirements. Expressing concern about the reduced demand for labor in particular, they define a “hypothetical scenario” for “functional upgrading” of the longer-lived products that can compensate for the jobs lost in manufacturing. This is a felt concern despite the fact that Japan’s population is contracting due to low rates of fertility, is aging rapidly, and experiences severe labor shortages (Japan Inc appears ill-prepared as labour shortages start to bite; INSIDE BUSINESS ASIA, 2018). However, it is in countries with youthful and expanding populations, high unemployment and large informal economies that loss of existing jobs is most problematic. Furthermore, this potential loss depends as much on decisions taken in other countries as domestic ones. The systems that will be put in place for material recovery and remanufacturing may be highly centralized and automated or decentralized and with labor-intensive technology components, facilitating creation of not only local jobs but also local governance. This is also the case for new energy systems and water systems and other forms of infrastructure. Engineering innovations are needed first and foremost for designing the kinds of systems that can satisfy both environmental and development objectives. These innovations comprise the content for the databases needed to represent scenarios for analysis using a framework like that described in this paper, an effort that depends upon some next steps in the collaboration between input-output economists and industrial ecologists.

5.3. Sustainable development Sustainable entails living within the earth’s means in terms of material resources and preventing degradation of earth systems critical for life. The development challenge is to reduce the historically great, destabilizing, and still expanding inequalities among the inhabitants of the planet, the aim of the UN Sustainable Development Goals. A global circular economy for materials is high on the list of priorities for a sustainable economic system, as are energy systems based on renewable sources and water systems that provide qualities adequate for different purposes though recovery and treatment of wastewater streams. However, meeting sustainability objectives does not assure progress in development. As the numerical examples in this paper suggest, approaches that are most successful in recovering value from used products at low cost do so by reducing the quantity of factor inputs required to satisfy a given volume of final demand. This is in general applicable for all factors – energy, metals, and other resources as well as capital and labor. We have also seen that recovery of products or materials may be an economic boon or a burden depending on the nature of processing that is involved. And finally the implications of a given global strategy

Appendix A. Sectors, Technologies, Factors of Production, Wastes, and Conversion Factors This appendix describes the sectors, technologies, factors of production, and wastes that figure in the scenarios. It also includes the values assumed for conversion factors related to the generation of wastes. Sectors and Technologies Sector 1. – Metal Extraction (ME). This sector has two alternative technologies to produce metals. Its output is measured in kg. Technology 1.1 – Virgin metals (VM) uses virgin ore Technology 1.2 – Recovered metals (RM) recovers metals from recycled used computers leaving waste in the form of a residue. Sector 2. – Computers (C) has two alternative technologies. Its output is measured in physical units, the number of computers produced. Technology 2.1 – New computers (NC) produces new computers Technology 2.2 – Remanufactured computers (RC) remanufactures used computers, leaving waste in the form of residue. Sector 3. – Other Machines (OM) represents the remainder of industrial production. It has a single technology and its output is measured in physical units, the number of machines produced. Technology 1.1 – Other Machines (OM) Sector 4. – Landfill (Lf) handles the disposal of waste and has a single technology. It provides this service to sectors 1 – 3. Its output is measured in m3, the volume of disposed waste. Technology 4.1 – Landfill (Lf). Factors of Production and Units 1 2 3 4

Labor (Lb): person-hours. Ore (O): tonnes (1 tonne = 1000 kg). Used Computers (UC): number of units. Land Volume for Landfill (LV): m3.

Wastes In scenarios involving an active landfill sector, all wastes must be landfilled. 1 Residue (Re). Its source is either recovery of metals or remanufacturing of computers: m3. 2 Waste computers (WC) consist of used computers that are not recycled. 432

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Notation The components of A* are denoted as a*i,j.k, measuring the intermediate input required from sector i to the kth technological option for sector j. For factor inputs contained in F*, the corresponding notation is f*i,j.k. For output from the kth technology of sector j, the notation is x*j.k. Domestic Final Demand for Landfill When landfilling is required, domestic final demand for landfill, y4, is determined endogenously as the number of waste computers (used computers that are not recovered). This is an endogenous rather than an exogenous quantity, and is determined by the amount of recycling that occurs. See discussion in the text. Waste-Related Conversion Factors a b c d

The The The The

volume of a waste computer is 0.20 m3 (v0). number of used computers required per kg of recovered metal produced is 5 (g). residue from the recovery of metal from one used computer is 0.15 m3 (v1). residue from the remanufacture of one used computer is 0.10 m3 (v2).

Appendix B. Single Region Analysis Appendix B shows the values of technical coefficients and exogenous variables under all scenarios in the one-region analysis of five scenarios and the scenario outcomes. Each scenario is calculated for three regions, and the landfill sector is active four of the scenarios. There is no trade among regions. For scenario A5, the second row in the A* matrix is reduced by half to represent the longer computer lifetime. The waste-related conversion factors are given at the end of Appendix A. Section B.1 shows the technical coefficients; section B.2 displays major results in Figures B1, B2, and B3; and section B.3 provides tables of scenario assumptions and results. Table B.1 A* and F* Matrices 4 Sector A* and F* Matrices for Scenarios A0, A1, A2,A4, and A5 Virgin Metals VM 1.1

Region 1

A*

F*

2

A*

F*

3

A*

F*

Metals Computers Other Machines Landfill Labor Ore Used Computers Land Volume Metals Computers Other Machines Landfill Labor Ore Used Computers Land Volume Metals Computers Other Machines Landfill Labor Ore Used Computers Land Volume

Recovered Metals RM 1.2

New Computers NC 2.1

Remanufactured Computers RC 2.2

Other Machines OM 3.1

Landfill Lf 4.1

M C OM

1 2 3

0.05 0.1 0.2

0.05 0.14 0.1

0.15 0.2 0.15

0.05 0.25 0.16

0.3 0.22 0.31

0 0.3 0.3

Lf

4

0

0.75

0

0.1

0

0

Lb O UC

1 2 3

3.2 2 0

3 0 5

1.5 0 0

1.1 0 1

1.2 0 0

1.2 0 0

LV

4

0

0

0

0

0

1

M C OM

1 2 3

0.01 0.01 0.1

0.05 0.14 0.1

0.25 0.35 0.26

0.05 0.25 0.16

0.3 0.15 0.25

0 0.1 0.1

Lf

4

0

0.75

0

0.1

0

0

Lb O UC

1 2 3

3 1 0

5 0 5

4 0 0

3 0 1

5 0 0

3 0 0

LV

4

0

0

0

0

0

1

M C OM

1 2 3

0.03 0.05 0.15

0.05 0.1 0.05

0.25 0.35 0.26

0.05 0.2 0.16

0.3 0.15 0.31

0 0.3 0.3

Lf

4

0

0.75

0

0.1

0

1

Lb O UC

1 2 3

6 1.5 0

5.5 0 5

4 0 0

2.2 0 1

2 0 0

1.2 0 0

LV

4

0

0

0

0

0

1

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B.2 Tables of Scenario Assumptions and Results Table B.2.1. Scenario A0 No Trade Model Scenario Name Scenario Description

Scenario A0 No Landfill No Recycling of of of of

Units

Economic Structure

No. No. No. No.

Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM)

y1 y2 y3

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC)

Region 1

Sectors Technologies(used) Factors(used) Waste Types

Region 2

Region 3

Sum

3 3 3 2

3 3 3 2

3 3 3 2

kg physical unit physical unit

0 50,000 6,000

0 1,000 500

0 100,000 10,000

0 151,000 16,500

f1 f2 f3

person-hour tonne physical unit

250,000 50,000 30,000

150,000 50,000 100

1,500,000 120,000 70,000

1,900,000 220,000 100,100

π1 π2 π3

$/person-hour $/kg $/physical unit

12.0 7.0 0.0

1.2 2.0 0.0

3.0 6.0 0.0

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Region 1

Region 2

Region 3

Z E

$ $

2,892,425 2,892,425

22,814 22,814

4,912,439 4,912,439

Sum 7,827,678 7,827,678

Outputs by Technology

Virgin Metals (VM) New Computers (NC) Other Machines (OM)

x11 x21 x31

kg physical unit physical unit

21,395 73,676 30,914

913 1,885 1,442

78,256 183,054 100,482

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM)

p1 p2 p3

$/kg $/physical unit $/physical unit

75.0 49.5 69.3

7.2 15.8 14.1

35.5 45.7 34.1

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC)

r1 r2 r3

$/person-hour $/tonne $/physical unit

0.0 0.0 0.0

0.0 0.0 0.0

0.0 0.0 0.0

Factor Use

Labor (Lb) Ore (O) Used Computers (UC)

fu1 fu2 fu3

person-hour tonne physical unit

216,074 42,790 0

17,490 913 0

1,402,713 117,384 0

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC)

fs1 fs2 fs3

person-hour tonne physical unit

33,926 7,210 30,000

134,411 49,087 100

97,287 2,617 70,000

265,624 58,914 100,100

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

0 6,000

0 20

0 14,000

0 20,020

Note. Factor use is measured in constant prices while factor earnings include rents.

434

100,564 258,615 132,838

1,636,277 161,087 0

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Table B.2.2. Scenario A1 No Trade Model Scenario Name Scenario Description

Scenario A1 Landfill No Recycling of of of of

Units

Economic Structure

No. No. No. No.

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill(Lf)

y1 y2 y3 y4

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Region 1

Sectors Technologies(used) Factors(used) Waste Types

Region 2

Region 3

Sum

4 4 4 2

4 4 4 2

4 4 4 2

kg physical unit physical unit m3

0 50,000 6,000 6,000

0 1,000 500 20

0 100,000 10,000 14,000

0 151,000 16,500 20,020

f1 f2 f3 f4

person-hour tonne physical unit m3

250,000 50,000 30,000 10,000

150,000 50,000 100 1,000

1,600,000 130,000 70,000 20,000

2,000,000 230,000 100,100 31,000

π1 π2 π3 π4

$/person-hour $/kg $/physical unit $/m3

12.0 7.0 0.0 10.0

1.2 2.0 0.0 5.0

3.0 6.0 0.0 10.0

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Region 1

Region 2

Region 3

Z E

$ $

3,252,648 3,252,648

23,046 23,046

5,437,874 5,437,874

Sum 8,713,568 8,713,568

Outputs by Technology

Virgin Metals (VM) New Computers (NC) Other Machines (OM) Landfill(Lf)

x11 x21 x31 x41

kg physical unit physical unit m3

23,186 77,222 34,812 6,000

915 1,889 1,446 20

84,055 192,477 111,380 14,000

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill (Lf)

p1 p2 p3 p4

$/kg $/physical unit $/physical unit $/m3

75.0 49.5 69.3 60.0

7.2 15.8 14.1 11.6

35.5 45.7 34.1 37.5

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

r1 r2 r3 r4

$/person-hour $/tonne $/physical unit m3

0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0

Factor Use

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

fu1 fu2 fu3 fu4

person-hour tonne physical unit m3

239,003 46,373 0 6,000

17,596 915 0 20

1,513,794 126,082 0 14,000

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

fs1 fs2 fs3 fs4

person-hour tonne physical unit m3

10,997 3,627 30,000 4,000

132,404 49,085 100 980

86,206 3,918 70,000 6,000

229,607 56,630 100,100 10,980

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

0 6,000

0 20

0 14,000

0 20,020

Note. Factor use is measured in constant prices while factor earnings include rents.

435

108,156 271,588 147,638 20,020

1,770,393 173,370 0 20,020

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Table B.2.3. Scenario A2 No Trade Model Scenario Name Scenario Description

Scenario A2 Landfill and Metal Recovery of of of of

Units

Economic Structure

No. No. No. No.

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill(Lf)

y1 y2 y3 y4

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Region 1

Sectors Technologies(used) Factors(used) Waste Types

Region 2

Region 3

Sum

4 5 4 2

4 5 4 2

4 5 4 2

kg physical unit physical unit m3

0 50,000 6,000 0

0 1,000 500 0

0 100,000 10,000 0

0 151,000 16,500 0

f1 f2 f3 f4

person-hour tonne physical unit m3

250,000 50,000 30,000 10,000

150,000 50,000 100 1,000

1,600,000 130,000 70,000 20,000

2,000,000 230,000 100,100 31,000

π1 π2 π3 π4

$/person-hour $/kg $/physical unit $/m3

12.0 7.0 0.0 10.0

1.2 2.0 0.0 5.0

3.0 6.0 0.0 10.0

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Region 1

Z E

$ $

30,34,530 32,50,530

Region 2

Region 3

23,043 23,043

5,153,776 5,297,957

897 20 1,893 1,447 15

68,503 14,000 190,773 106,850 10,500

Sum 8,211,349 8,571,530

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Other Machines (OM) Landfill(Lf)

x1.1 x1.2 x2.1 x3.1 x4.1

kg kg physical unit physical unit

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill (Lf)

p1 p2 p3 p4

$/kg $/physical unit $/physical unit $/m3

75.0 49.5 69.3 60.0

7.2 15.8 14.1 11.6

35.5 45.7 34.1 37.5

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

r1 r2 r3 r4

$/person-hour $/tonne $/physical unit

0.0 0.0 7.2 0.0

0.0 0.0 0.04 0.0

0.0 0.0 4.1 0.0

Factor Use

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

fu1 fu2 fu3 fu4

person-hour tonne physical unit m3

229,952 32,872 30,000 4,500

17,644 897 100 15

1,477,415 102,755 70,000 10,500

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

fs1 fs2 fs3 fs4

person-hour tonne physical unit m3

20,048 17,128 0 5,500

132,356 49,103 0 985

122,525 27,245 0 9,500

274,929 93,476 0 15,985

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

15 0

10,500 0

15,015

Note. Factor use is measured in constant prices while factor earnings include rents.

436

16,436 6,000 76,334 32,880 4,500

4,500 0

85,836 20,020 269,000 141,177 15,015

1,725,011 136,524 100,100 15,015

0

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Table B.2.4. Scenario A4 Note: Scenario A3, computer remanufacturing only, is not shown as it produces results identical to Scenario A4. No Trade Model Scenario Name Scenario Description

Scenario A4 Landfill, Metal Recovery, and Computer Remanufacturing Units

Economic Structure

No. No. No. No.

of of of of

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill(Lf)

y1 y2 y3 y4

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Region 1

Sectors Technologies Factors Waste Types

Region 3

Sum

3 6 4 2

3 6 4 2

3 6 4 2

kg physical unit physical unit m3

0 50,000 6,000 0

0 1,000 500 0

0 100,000 10,000 0

0 151,000 16,500 0

f1 f2 f3 f4

person-hour tonne physical unit m3

250,000 50,000 30,000 10,000

150,000 50,000 100 1,000

1,600,000 130,000 70,000 20,000

2,000,000 230,000 100,100 31,000

π1 π2 π3 π4

$/person-hour $/kg $/physical unit $/m3

12.0 7.0 0.0 10.0

1.2 2.0 0.0 5.0

3.0 6.0 0.0 10.0

Region 1

Region 2

Results of Scenario Computations

Units

Total Factor Use (objective function) Total Factor Earnings

Region 2

Region 3

Z E

$ $

2,798,764 3,251,742

22,367 23,050

3,582,346 5,342,137

x1.1 x1.2 x2.1 x2.2 x3.1 x4.1

kg kg physical unit physical unit physical unit

19,334 0 46,926 30,000 32,762 3,000

881 0 1,766 100 1,419 10

52,595 0 93,533 70,000 80,446 7,000

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Remanufactured Computers (RC) Other Machines (OM) Landfill (Lf)

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill (Lf)

p1 p2 p3 p4

$/kg $/physical unit $/physical unit $/m3

75.0 49.5 69.3 60.0

7.2 15.8 14.1 11.6

35.5 45.7 34.1 37.5

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

r1 r2 r3 r4

$/person-hour $/tonne $/physical unit $/m3

0.0 0.0 15.1 0.0

0.0 0.0 6.8 0.0

0.0 0.0 26.5 0.0

Factor Use

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

fu1 fu2 fu3 fu4

person-hour tonne physical unit m3

208,174 38,669 30,000 3,000

17,179 881 100 10

1,012,997 78,893 70,000 7,000

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

fs1 fs2 fs3 fs4

person-hour tonne physical unit m3

41,826 11,331 0 7,000

132,871 49,119 0 990

587,003 51,107 0 13,000

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

3,000 0

10 0

7,000 0

Note. Factor use is measured in constant prices while factor earnings include rents.

437

Sum 6,403,477 8,616,929 72,810 0 142,225 100,100 114,627 10,010

1,238,350 118,443 100,100 10,010 761,700 111,557 0 20,990 10,010 0

Resources, Conservation & Recycling 145 (2019) 422–447

F. Duchin and S.H. Levine

Table B.2.5. Scenario A5 No Trade Model Scenario Name Scenario Description

Scenario A5 Landfill Metal Recovery Computer Remanufacturing Double Computer Lifetime of of of of

Units

Economic Structure

No. No. No. No.

Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill(Lf)

y1 y2 y3 y4

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Region 1

Sectors Technologies Factors Waste Types

Region 2

Region 3

Sum

4 6 4 2

4 6 4 2

4 6 4 2

kg physical unit physical unit m3

0 25,000 6,000 0

0 500 500 0

0 50,000 10,000 0

0 75,500 16,500 0

f1 f2 f3 f4

person-hour tonne physical unit m3

250,000 50,000 15,000 10,000

150,000 50,000 50 1,000

1,600,000 130,000 35,000 20,000

2,000,000 230,000 50,050 31,000

π1 π2 π3 π4

$/person-hour $/kg $/physical unit $/m3

12.0 7.0 0.0 10.0

1.2 2.0 0.0 5.0

3.0 6.0 0.0 10.0

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Z E

$ $

x1.1 x1.2 x2.1 x2.2 x3.1 x4.1

kg kg physical unit physical unit physical unit m3

Region 1

Region 2

Region 3

Sum

12,95,063 15,18,566

11,641 11,915

1,402,208 2,091,720

2,708,912 3,622,201

9,392 0 16,300 15,000 19,092 1,500

457 0 644 50 962 5

20,862 0 27,232 35,000 38,927 3,500

30,711 0 44,176 50,050 58,981 5,005

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Remanufactured Computers (RC) Other Machines (OM) Landfill (Lf)

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill (Lf)

p1 p2 p3 p4

$/kg $/physical unit $/physical unit $/m3

69.5 41.2 57.6 47.9

6.9 11.7 11.9 10.4

32.8 32.8 26.5 26.5

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

r1 r2 r3 r4

$/person-hour $/tonne $/physical unit $/m3

0.0 0.0 14.9 0.0

0.0 0.0 5.4 0.0

0.0 0.0 19.7 0.0

Factor Use

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

fu1 fu2 fu3 fu4

person-hour tonne physical unit m3

95,714 18,784 15,000 1,500

8,919 457 50 5

393,151 31,293 35,000 3,500

497,784 50,534 50,050 5,005

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill (LV)

fs1 fs2 fs3 fs4

person-hour tonne physical unit m3

154,286 31,216 0 8,500

141,081 49,543 0 995

1,206,849 98,707 0 16,500

1,502,216 179,466 0 25,995

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

1,500 0

5 0

3,500 0

5,005 0

Note. Factor use is measured in constant prices while factor earnings include rents.

438

Resources, Conservation & Recycling 145 (2019) 422–447

F. Duchin and S.H. Levine

Appendix C. No Trade and World Trade Scenarios Appendix C shows the values of technical coefficients and exogenous variables used in the no-trade and world trade (global) comparisons under three scenarios. The waste-related conversion factors are given at the end of Appendix A. Section C.1 shows the technical coefficients; section B.2 displays major results in Figures C1, C2, and C3; and section C.3 provides tables of scenario assumptions and results. Table C.1 A* and F* Matrices 3 Sector A* and F* Matrices Virgin Metals VM

Region 1

2

3

Recovered Metals RM

New Computers NC

Remanufactured Computers RC

Other Machines OM

A*

Metals Computers Other Machines

M C OM

1 2 3

1.1 0.05 0.1 0.2

1.2 0.05 0.14 0.1

2.1 0.2 0.3 0.2

2.2 0.05 0.25 0.16

3.1 0.3 0.22 0.31

F*

Labor Ore Used Computers

Lb O UC

1 2 3

3.2 2 0

3 0 5

1.5 0 0

1.1 0 1

1.2 0 0

A*

Metals Computers Other Machines

M C OM

1 2 3

0.01 0.01 0.1

0.05 0.14 0.1

0.25 0.35 0.26

0.05 0.25 0.16

0.3 0.15 0.25

F*

Labor Ore Used Computers

Lb O UC

1 2 3

3 1 0

5 0 5

4 0 0

3 0 1

5 0 0

A*

Metals Computers Other Machines

M C OM

1 2 3

0.03 0.05 0.15

0.05 0.1 0.05

0.25 0.35 0.26

0.05 0.2 0.16

0.2 0.15 0.31

F*

Labor Ore Used Computers

Lb O UC

1 2 3

6 1.5 0

5.5 0 5

4 0 0

2.2 0 1

2 0 0

439

Resources, Conservation & Recycling 145 (2019) 422–447

F. Duchin and S.H. Levine

C.2 Tables of Scenario Assumptions and Results C.2.1 No Trade ScenariosTable C.2.1.1. Scenario W0. No Trade Model Scenario Name Scenario Description

Scenario W0 No recycling of of of of

Units

Economic Structure

No. No. No. No.

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM)

y1 y2 y3

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC)

Region 1

Sectors Technologies Factors Waste Types

Region 2

Region 3

Sum

3 3 3 2

3 3 3 2

3 3 3 2

kg physical unit physical unit

0 50,000 6,000

0 1,000 500

0 100,000 10,000

0 151,000 16,500

f1 f2 f3

person-hour tonne physical unit

250,000 50,000 30,000

150,000 50,000 100

1,500,000 120,000 70,000

1,900,000 220,000 100,100

π1 π2 π3

$/person-hour $/kg $/physical unit

12.0 7.0 0.0

1.2 2.0 0.0

3.0 6.0 0.0

Region 1

Region 2

Region 3

Sum

2,892,425 2,892,425

22,814 22,814

4,912,439 4,912,439

7,827,678 7,827,678

21,395 0 73,676 0 30,914

913 0 1,885 0 1,442

78,256 0 183,054 0 100,482

100,564 0 258,615 0 132,838

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Z E

$ $

x1.1 x1.2 x2.1 x2.2 x3.1

kg kg physical unit physical unit physical unit

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Remanufactured Computers (RC) Other Machines (OM)

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM)

p1 p2 p3

$/kg $/physical unit $/physical unit

75.0 49.5 69.3

7.2 15.8 14.1

35.5 45.7 34.1

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC)

r1 r2 r3

$/person-hour $/tonne $/physical unit

0.0 0.0 0.0

0.0 0.0 0.0

0.0 0.0 0.0

Factor Use

Labor (Lb) Ore (O) Used Computers (UC)

fu1 fu2 fu3

person-hour tonne physical unit

216,074 42,790 0

17,490 913 0

1,402,713 117,384 0

1,636,277 161,087 0

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC)

fs1 fs2 fs3

person-hour tonne physical unit

33,926 7,210 30,000

132,510 49,087 100

97,287 2,617 70,000

263,723 58,914 100,100

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

0 6,000

0 20

0 14,000

0 20,020

Note. Factor use is measured in constant prices while factor earnings include rents.

440

Resources, Conservation & Recycling 145 (2019) 422–447

F. Duchin and S.H. Levine

Table C.2.1.2 Scenario W1 No Trade Model Scenario Name Scenario Description

Scenario W1 Metal Recovery Only of of of of

Units

Sectors Technologies(used) Factors(used) Waste Types

Region 1

Region 2

Region 3

3 4 3 2

3 4 3 2

3 4 3 2

Sum

Economic Structure

No. No. No. No.

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM)

y1 y2 y3

kg physical unit physical unit

0 50,000 6,000

0 1,000 500

0 100,000 10,000

0 151,000 16,500

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC)

f1 f2 f3

person-hour tonne physical unit

250,000 50,000 30,000

150,000 50,000 100

1,500,000 120,000 70,000

1,900,000 220,000 100,100

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC)

π1 π2 π3

$/person-hour $/kg $/physical unit

Results of Scenario Computations

Units

Total Factor Use (objective function) Total Factor Earnings

Z E

$ $

12.0 7.0 0.0

1.2 2.0 0.0

3.0 6.0 0.0

Region 1

Region 2

Region 3

Sum

2,764,363 2,893,390

22,814 22,814

4,759,700 4,913,692

7,546,877 7,829,896

15,093 6,000 73,675 29,956

913 0 1,885 1,442

64,154 14,000 183,706 98,677

80,160 20,000 259,266 130,075

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Other Machines (OM)

x1.1 x1.2 x2.1 x3.1

kg kg physical unit physical unit

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM)

p1 p2 p3

$/kg $/physical unit $/physical unit

75.0 49.5 69.3

7.2 15.8 14.1

35.5 45.7 34.1

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC)

r1 r2 r3

$/person-hour $/tonne $/physical unit

0.0 0.0 4.3

0.0 0.0 0.0

0.0 0.0 2.2

Factor Use

Labor (Lb) Ore (O) Used Computers (UC)

fu1 fu2 fu3

person-hour tonne physical unit

212,756 30,185 30,000

17,490 913 0

1,394,104 96,231 70,000

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC)

fs1 fs2 fs3

person-hour tonne physical unit

37,245 19,815 0

132,510 49,087 100

105,896 23,769 0

275,651 92,671 100

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

4,500 0

0 20

10,500 0

15,000 20

Note. Factor use is measured in constant prices while factor earnings include rents.

441

1,624,350 127,329 100,000

Resources, Conservation & Recycling 145 (2019) 422–447

F. Duchin and S.H. Levine

Table C.2.1.3. Scenario W2 No Trade Model Scenario Name Scenario Description

Scenario W2 Both Recycling Options of of of of

Units

Economic Structure

No. No. No. No.

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM)

y1 y2 y3

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC)

Region 1

Sectors Technologies(used) Factors(used) Waste Types

Region 2

Region 3

Sum

3 5 3 2

3 5 3 2

3 5 3 2

kg physical unit physical unit

0 50,000 6,000

0 1,000 500

0 100,000 10,000

f1 f2 f3

person-hour tonne physical unit

250,000 50,000 30,000

150,000 50,000 100

1,500,000 120,000 70,000

π1 π2 π3

$/person-hour $/kg $/physical unit

12.0 7.0 0.0

1.2 2.0 0.0

3.0 6.0 0.0

0 151,000 16,500 1,900,000 220,000 100,100

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Region 1

Region 2

Region 3

Z E

$ $

2,618,652 2,879,324

22,251 22,817

3,319,628 4,915,638

x1.1 x1.2 x2.1 x2.2 x3.1

kg kg physical unit physical unit physical unit

18,439 0 45,153 30,000 30,813

880 0 1,764 100 1,417

49,696 0 88,822 70,000 74,997

Sum 5,960,531 7,817,779

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Remanufactured Computers (RC) Other Machines (OM)

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM)

p1 p2 p3

$/kg $/physical unit $/physical unit

75.0 49.5 69.3

7.2 15.8 14.1

35.5 45.7 34.1

Factor Rent

Labor (Lb) Ore (O) Used Computers (UC)

r1 r2 r3

$/person-hour $/tonne $/physical unit

0.0 0.0 9.1

0.0 0.0 5.6

0.0 0.0 22.8

Factor Use

Labor (Lb) Ore (O) Used Computers (UC)

fu1 fu2 fu3

person-hour tonne physical unit

196,709 36,877 30,000

17,076 880 100

957,456 74,543 70,000

1,171,241 112,300 100,100

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC)

fs1 fs2 fs3

person-hour tonne physical unit

53,291 13,123 0

132,924 49,120 0

542,544 45,457 0

728,759 107,700 0

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

3,000 0

10 0

7,000 0

Note. Factor use is measured in constant prices while factor earnings include rents.

442

69,015 0 135,739 100,100 107,227

10,010 0

Resources, Conservation & Recycling 145 (2019) 422–447

F. Duchin and S.H. Levine

C.2.2 World Trade Scenarios C.2.2.1 Scenario W0 World Trade Model Scenario Name Scenario Description

Scenario W0 No Recycling of of of of

Units

Economic Structure

No. No. No. No.

Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM)

y1 y2 y3

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC)

Region 1

Sectors Technologies (in use) Factors (in use) Waste Types

Region 2

Region 3

Sum

3 5 3 2

3 5 3 2

3 5 3 2

kg physical unit physical unit

0 50,000 6,000

0 1,000 500

0 100,000 10,000

f1 f2 f3

person-hour tonne physical unit

250,000 50,000 30,000

150,000 50,000 100

1,500,000 120,000 70,000

π1 π2 π3

$/person-hour $/kg $/physical unit

12.0 7.0 0.0

1.2 2.0 0.0

3.0 6.0 0.0

0 151,000 16,500 1,900,000 220,000 100,100

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Region 1

Region 2

Region 3

Sum

Z E

$ $

3,000,000 4,350,009

280,000 1,560,000

1,545,228 1,545,228

x1.1 x1.2 x2.1 x2.2 x3.1

kg kg physical unit physical unit physical unit

0 0 166,667 0 0

50,000 0 0 0 0

15,234 0 49,764 0 89,455

4,825,228 7,455,237

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Remanufactured Computers (RC) Other Machines (OM)

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM)

p1 p2 p3

$/kg $/physical unit $/physical unit

35.5 45.7 34.1

35.5 45.7 34.1

35.5 45.7 34.1

Factor Rents

Labor (Lb) Ore (O) Used Computers (UC)

r1 r2 r3

$/person-hour $/tonne $/physical unit

5.4 0.0 0.0

1.8 20.2 0.0

0.0 0.0 0.0

Factor Use

Labor (Lb) Ore (O) Used Computers (UC)

fu1 fu2 fu3

person-hour tonne physical unit

250,000 0 0

150,000 50,000 0

469,373 22,852 0

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC)

fs1 fs2 fs3

person-hour tonne physical unit

0 50,000 30,000

0 0 100

1,030,627 97,148 70,000

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

0 6,000

0 20

0 14,000

Net Exports

Metal Extraction (ME) Computers (C) Other Machines (OM)

ne1 ne2 ne3

kg physical unit physical unit

−25,000 83,333 −31,000

49,500 −1,500 −5,500

−24,500 −81,833 36,500

0 0 0

$1,867,935

1,499,415

−3,367,350

0

−25,000 133,333 −25,000

49,500 −500 −5,000

−24,500 18,167 46,500

Balance of Trade Domestic Final Demand plus Net Exports

Metal Extraction (ME) Computers (C) Other Machines (OM)

d1 d2 d3

kg physical unit physical unit

Note. Factor use is measured in constant prices while factor earnings include rents.

443

65,234 0 216,431 0 89,455

869,373 72,852 0 1,030,627 147,148 100,100 0 20,020

0 151,000 16,500

Resources, Conservation & Recycling 145 (2019) 422–447

F. Duchin and S.H. Levine

Table C.2.2.2 Scenario W1 World Trade Model Scenario Name Scenario Description

Scenario W1 Metal Recovery Only of of of of

Units

Economic Structure

No. No. No. No.

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM)

y1 y2 y3

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC)

Region 1

Sectors Technologies (in use) Factors (in use) Waste Types

Region 2

Region 3

Sum

3 5 3 2

3 5 3 2

3 5 3 2

kg physical unit physical unit

0 50,000 6,000

0 1,000 500

0 100,000 10,000

f1 f2 f3

person-hour tonne physical unit

250,000 50,000 30,000

150,000 50,000 100

1,500,000 120,000 70,000

π1 π2 π3

$/person-hour $/kg $/physical unit

12.0 7.0 0.0

1.2 2.0 0.0

3.0 6.0 0.0

0 151,000 16,500 1,900,000 220,000 100,100

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Z E x1.1 x1.2 x2.1 x2.2 x3.1

Region 1

Region 2

Region 3

Sum

$ $

3,000,000 4,350,009

280,000 1,565,000

1,392,488 1,546,495

kg kg physical unit physical unit physical unit

0 0 166,667 0 0

50,000 0 0 0 0

1,133 14,000 50,417 0 87,650

4,672,488 7,461,504

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Remanufactured Computers (RC) Other Machines (OM)

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM)

p1 p2 p3

$/kg $/physical unit $/physical unit

35.5 45.7 34.1

35.5 45.7 34.1

35.5 45.7 34.1

Factor Rents

Labor (Lb) Ore (O) Used Computers (UC)

r1 r2 r3

$/person-hour $/tonne $/physical unit

5.4 0.0 0.0

3.6 14.9 0.0

0.0 0.0 2.2

Factor Use

Labor (Lb) Ore (O) Used Computers (UC)

fu1 fu2 fu3

person-hour tonne physical unit

250,000 0 0

150,000 50,000 0

460,764 1,700 70,000

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC)

fs1 fs2 fs3

person-hour tonne physical unit

0 50,000 30,000

0 0 100

1,039,236 118,301 0

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

0 6,000

0 20

10,500 0

Net Exports

Metal Extraction (ME) Computers (C) Other Machines (OM)

ne1 ne2 ne3

kg physical unit physical unit

−25,000 83,333 −31,000

49,500 −1,500 −5,500

−24,500 −81,833 36,500

0 0 0

$

1,867,935

1,499,415

−3,367,350

0

kg physical unit physical unit

−25,000 133,333 −25,000

49,500 −500 −5,000

−24,500 18,167 46,500

Balance of Trade Domestic Final Demand plus Net Exports

Metal Extraction (ME) Computers (C) Other Machines (OM)

d1 d2 d3

Note. Factor use is measured in constant prices while factor earnings include rents.

444

51,133 14,000 217,084 0 87,650

860,764 51,700 70,000 1,039,236 168,301 30,100 10,500 6,020

0 151,000 16,500

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Table C.2.2.3 Scenario W2 World Trade Model Scenario Name Scenario Description

Scenario W2 Both Recycling Options of of of of

Units

Economic Structure

No. No. No. No.

Domestic Final Demand (y)

Metal Extraction (ME) Computers (C) Other Machines (OM)

y1 y2 y3

Factor Endowments (f)

Labor (Lb) Ore (O) Used Computers (UC)

Factor Prices (π)

Labor (Lb) Ore (O) Used Computers (UC)

Region 1

Sectors Technologies (in use) Factors (in use) Waste Types

Region 2

Region 3

Sum

3 5 3 2

3 5 3 2

3 5 3 2

kg physical unit physical unit

0 50,000 6,000

0 1,000 500

0 100,000 10,000

f1 f2 f3

person-hour tonne physical unit

250,000 50,000 30,000

150,000 50,000 100

1,500,000 120,000 70,000

π1 π2 π3

$/person-hour $/kg $/physical unit

12.0 7.0 0.0

1.2 2.0 0.0

3.0 6.0 0.0

0 151,000 16,500 1,900,000 220,000 100,100

Results of Scenario Computations Units Total Factor Use (objective function) Total Factor Earnings

Region 1

Region 2

Region 3

Sum

Z E

$ $

2,242,606 2,374,602

269,937 480,925

926,025 1,794,022

x1.1 x1.2 x2.1 x2.2 x3.1

kg kg physical unit physical unit physical unit

0 0 102,589 30,000 0

44,969 0 3,698 100 0

0 0 0 70,000 77,337

3,438,568 4,649,549

Outputs by Technology

Virgin Metals (VM) Recovered Metals (RM) New Computers (NC) Remanufactured Computers (RC) Other Machines (OM)

Sector Prices

Metal Extraction (ME) Computers (C) Other Machines (OM)

p1 p2 p3

$/kg $/physical unit $/physical unit

12.1 28.6 20.2

12.1 28.6 20.2

12.1 28.6 20.2

Factor Rents

Labor (Lb) Ore (O) Used Computers (UC)

r1 r2 r3

$/person-hour $/tonne $/physical unit

0.0 0.0 4.4

1.4 0.0 9.9

0.0 0.0 12.4

Factor Use

Labor (Lb) Ore (O) Used Computers (UC)

fu1 fu2 fu3

person-hour tonne physical unit

186,884 0 30,000

150,000 44,969 100

308,675 0 70,000

Factor Surplus

Labor (Lb) Ore (O) Used Computers (UC)

fs1 fs2 fs3

person-hour tonne physical unit

63,116 50,000 0

0 5,031 0

1,191,325 120,000 0

Wastes

Residues (Re) Waste Computers (WC)

w1 w2

m3 m3

3,000 0

10 0

7,000 0

Net Exports

Metal Extraction (ME) Computers (C) Other Machines (OM)

ne1 ne2 ne3

kg physical unit physical unit

−16,888 54,571 −26,188

43,589 1,029 −5,974

−26,701 −55,600 32,162

0 0 0

$

825,054

438,003

−1,263,057

0

kg physical unit physical unit

−16,888 104,571 −20,188

43,589 2,029 −5,474

−26,701 44,399 42,163

Balance of Trade Domestic Final Demand plus Net Exports

Metal Extraction (ME) Computers (C) Other Machines (OM)

d1 d2 d3

Note. Factor use is measured in constant prices while factor earnings include rents.

445

44,969 0 106,287 100,100 77,337

645,559 44,969 100,100 1,254,441 175,031 0 10,010 0

0 150,999 16,501

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Appendix D. Shadow Prices and Rents in RCOT Section 5.2 discusses the relationship in the current implementation of the RCOT model between shadow prices in linear programming and economic rents. For variables subject to binding constraints, a linear program determines a shadow price that measures by how much an objective function would be increased if there were one more unit of a scarce factor. Since our objective is to minimize the factor costs (see below), a negative shadow price indicates that benefit is derived from an additional unit of the constrained factor. In earlier RCOT applications, the rent earned on a scarce factor is simply equal to the negative of the shadow price. However, when actions are imposed by regulation, as in the case where landfilling of used computers is required, the rent on used computers is the sum of two components: the negative of the shadow price, as is typical, plus the potential benefit, always positive, of not having to landfill the used computer (since it is being recycled). The reason for the added complexity is that the LP solution, which usually reflects the economic choice criterion represented by the objective function alone, now must also respect a nondiscretionary obligation, in this case the requirement to landfill any end-of-life object that is not recovered. There are three possibilities for the value of the resulting rent: (1) the shadow price is positive, meaning a negative contribution to the rent, but this negative value is more than compensated by the benefit from avoiding landfilling; (2) the shadow price is negative and thus the rent is positive; and (3) the shadow price is positive, and the benefit of avoiding landfilling cannot compensate for it. In the first two cases the used computer will be recycled, but in the third it will be landfilled. Note that a reduction in the cost of landfilling could change the outcome from recycling to landfilling. We believe this more complex expression for the relation between the shadow price and the scarcity rent, which is utilized for the first time in this application, will provide valuable insights when the analysis moves from our illustrative database to one that is empirically grounded. The objective function of the RCOT primal minimizes use of factors weighted by (ex ante) factor prices, Z = πTFx. At the optimum Zopt = Wopt, where the dual objective function is W = pTy − rTf =Σjpjyj − Σkrkfk. The shadow price of the ith factor, si, is the increase in Wopt due to the increase by one unit of the ith factor. If the variables y and f are independent and exogenous, then the shadow price of the ith factor in RCOT is si = {Σjpjyj − Σk≠irkfk − ri(fi+1)} − {Σjpjyj − Σk≠irkfk − rifi} = −ri, and the shadow price of the factor is the negative of the rent associated with that factor. However, recall (from Section 3.2) that in the example presented in this paper y4 = v0[f3 − (f *3,1.2 x*1.2) − x*2.2]; y4 is thus endogenous and dependent on f3. In this case, s3 = {Σj≠4pjyj + v0[f3 + 1 − (f *3,1.2 x*1.2) − x*2.2]p4 − Σk≠3rkfk − r3(f3+1)} − {Σj≠4pjyj + v0[f3 − (f *3,1.2 x*1.2) − x*2.2]p4 − Σk≠3rkfk − r3f3} = p4v0 − r3. Rearranging, r3 = −s3 + p4v0. The term p4v0 is precisely the cost associated with treating a used computer as waste and landfilling it; that is, it is the potential benefit, always positive, of not having to landfill the used computer if it is recycled. For example, let us consider region 1 under Scenario A2. Under this scenario recycled used computers can be used only for recovery of metal. The shadow price for used computers is the increase in the objective function if the number of used computers is increased by one (1); it is calculated by the RCOT primal as s3 = $4.74. Alternatively, this value can be obtained from the difference in cost of producing one kg of metal from used computers versus producing it from virgin ore, shown in Table D.1. (The cost of an intermediate or factor input is computed by multiplying its unit price by the corresponding coefficient in A* or F*. As an example, the first row of the Table D.1 shows that the price of a kg of metal is 74.95 and that 0.05 kg of metal are needed to produce an additional kg of metal from either virgin ore or recovered computers, resulting in a cost for this input of $74.95* 0.05 = $3.75). Table D.1 Cost Breakdowns for Producing 1 kg of Metal under Scenario A2 Prices and Costs in USD Virgin Ore Metal Goods Metal Extraction (ME) Computers (C) Other Machines (OM) Landfill (Lf) Factors Labor (Lb) Ore (O) Used Computers (UC) Land Volume for Landfill(LV)

Recovered Metal

Good Prices

A* Coefficient

Cost

A* Coefficient

Cost

$74.95 $49.54 $69.25 $60.04

0.05 0.10 0.20 0.00

$3.75 $4.95 $13.85 $0.00

0.05 0.14 0.10 0.75

$3.75 $6.94 $6.93 $45.03

Factor Prices

F* Coefficient

Cost

F* Coefficient

Cost

$12.00 $7.00 $0.00 $10.00

3.20 2.00 0.00 0.00 Total Cost

$38.40 $14.00 $0.00 $0.00 $74.95

3.00 0.00 5.00 0.00

$36.00 $0.00 $0.00 $0.00 $98.64

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Since each used computer yields 0.2 kg of metal (see conversion factors in Appendix A), the shadow price for a used computer is s3 = 0.2*($98.64 - $78.95) = $4.74. However, since the price of landfill is p4 = $60/m3 and v0 = 0.2 m3 (see Appendix A), each used computer not recycled would result in a $12.00 landfill cost; thus the rent is r3 = -$4.74 + $12.00 = $7.26 Note that the positive shadow price corresponds to metal recovery from used computers operating at a loss, as discussed in Section 3.3. However, the benefit from avoiding landfill is of adequate magnitude to result in a positive rent, indicating that recycling of used computers for metal recovery should be performed (as noted in Section 5.2). If the landfill cost per waste computer were lower than the shadow price then the rent would be negative, indicating that all used computers would be treated as waste and landfilled in the absence of regulations to the contrary. This is precisely the case for regions 1 and 3 under scenario W1: no landfilling is required, so its cost is zero

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