An assessment of the European regulation on battery recycling for electric vehicles 

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With development difficulties of specific markets and industries, recycled inputs struggle to compete with regular inputs in production, especially when high recycling rates bear significant costs. However, accounting for social costs from resource extraction, use and end-of-life of products, could change the trade-off between extraction and recycling. Al-though recycling is usually, and correctly, noted as an opportunity to reduce the impact of consumption on primary resources and waste, we also consider in this chapter the possible negative environmental consequences of recycling and we discuss the resulting arbitrations. We discuss the policy implications, and we highlight the existence of standard environmental externalities as well as a positive externality linked to the absence of a market for waste.


The early economic studies on secondary materials long focused on recycling’s ability to save extracted resources (UNEP, 2019). More recently, however, economists have begun to consider recycling’s ability to mitigate waste pollution and greenhouse gas (GHG) emissions. With this new view, the concept of a circular economy, in which recycling is one of the cor-nerstones, appeared as a solution for a more sustainable economical model, as formalized by Braungart and McDonough (2002) in Cradle to Cradle. This concept has generated a significant amount of ”grey literature” through many non-governmental organizations like the Ellen McArthur Foundation. It can be noted that a large concentration of the grey liter-ature, as well as of the academic literature, occurs in Europe and Asia. Both of these regions have many academic and institutional initiatives in this field (de Jesus and Mendon¸ca, 2018).
In this chapter, we contribute to the literature on circular economy by examining the impact of recycling in an industrial sector facing environmental, resource and climate con-straints. In this context, we must consider three different balances: a material balance in order to examine the saving of natural resources and the reduction of waste accumulation; a carbon balance for the topic of climate change; and, an economic balance for the evolution of consumption. Hence, we see environmental objectives of recycling going in three different directions: the saving of natural resources while its shortage could lead to economic diffi-culties; the reduction of waste accumulation that is costly to manage for both public and private entities, and poses a threat to the environment; the fight against climate change and especially the reduction of GHG emissions. A good illustration of these features can be found in the metal sector: scarcity of critical metals raises the question of their sustainable use and end of life management, as well as the emissions rates of their lifecycle (UNEP, 2011).
One intended specificity of this chapter is to extend the study of recycling by considering climate change as an additional externality. Recycling can indeed harm the environment, in particular because of the extra energy required by this activity and its resulting po-tential GHG emissions. This additional externality leads to new arbitrations we describe in the model: in most cases, recycling is a way of reducing the use of resources with a high carbon footprint (ADEME and FEDEREC, 2017), but recycling is still the source of GHG emissions. It has already been highlighted that circularity and environmental issues are connected in an industrial sector, with for instance used tires (Lonca et al., 2018). In France, studies of ADEME and FEDEREC (2017), ADEME and Bio by Deloitte (2017) and ADEME (2019) focused on quantifying different impacts of recycling in terms of GHG emissions, showing that industrial processes are often highly carbon intensive compared to recycling industries (see Table 1). However, in the end, recycling does not appear to be the ideal clean substitute to regular production: recycling produces its own emissions; there is a need in initial production from a regular source; and, recycling comes with a cost (UNEP, 2011). These environmental considerations contribute to the current policy framework, with many countries implementing emissions reduction targets that affect polluting industries.
In order to clearly understand their various effects, we successively introduce two negative environmental externalities. First, we examine waste accumulation that harms the economy through a specific damage function, and then we add cumulative GHG emissions that are constrained by an exogenous carbon budget. Consequently, we observe that a third source of (positive) externality must also be considered as long as there is no waste market, as consumption of the final good provided a waste stream which can be reused thanks to an endogenous effort of recycling.
In this framework, we characterize the main properties of the optimal trajectories of the model. In particular, we discuss the merit order in using each type of resource, depending on the relative scarcity of resources and their emissions rates. We analyze the optimized recycling rate curve through time and we show that, under some conditions, it can be an inverted U-shape. We also discuss the respective dynamics of resource use, which sometimes can result in a catch-up phase of consumption at the end of the program. Last, we show that in a competitive market economy, this optimal outcome can be implemented by a set of tax-subsidy schemes and we discuss their policy implications depending on the identity of the tax payer or the subsidy beneficiary. The introduction of a waste market allows to account for the positive externality linked to production that relaxes resources restriction thanks to recycling. This externality comes from the dynamic framework of the model and has not been considered by the static economic literature on recycling.
The rest of this chapter is organized as follows. Section 1.2 provides a brief review of the literature on recycling. Section 1.3 characterizes the basic model and describes the different possible scenarios of consumption and recycling. Section 1.4 considers the introduction of GHG emissions through an emissions ceiling.1 Section 1.5 studies the decentralized equilib-rium outcome and discusses policy implications. Section 1.6 concludes.
1We also propose three other extensions in appendix: accounting for a scrap value for waste, decoupling emissions between collection and transformation in the recycling branch, limiting the capacity of the recycling sector.

Related literature

Our work can be related to three strands of literature on recycling: resource scarcity, waste management, and environmental policies.
Early studies from the 70s-80s already tackled resource scarcity. For instance, Smith (1972) puts forward social costs linked to waste accumulation and stock diminution. He focuses on the dynamics of waste when recycling is under consideration, and he shows that there is a trade-off between private costs (labor, material) and social costs (waste accumu-lation, resource depletion). Such dynamic models informed the first economic guidelines motivating recycling. Waste accumulation issues were added to the topic through various models intending to find the optimal level of pollution in an economy (see for instance Plourde (1972), Forster (1973), or Hoel (1978)). Later, the work of Chakravorty et al. (2006) and Chakravorty et al. (2008) focused on the order of resource extraction and gave many insights on situations where resource depletion induces pollution, that changes the extraction order. However, these studies do not include recycling in their model.
An important part of the relevant literature was later developed around the topic of using green policies to promote recycling. Palmer and Walls (1997) use a static micro-economic model to analyze the effects of diverse economic incentives such as subsidies, waste tax and deposit-refunds. This approach gives many policy insights but only takes into account waste and recycling activities. The work started by Palmer and Walls (1997) was then expanded to include environmental effects associated with recycling and resource extraction (Fullerton and Kinnaman, 1995; Palmer et al., 1997). Going further in this type of analysis, Walls and Palmer (2001) integrate life-cycle aspects of production and consumption and discuss optimal policy instruments. However, they only include an effluent linked to a third, non-material, input in production. Thus they do not differentiate between recycling and extraction. In a later work, Acuff and Kaffine (2013) add carbon emissions to the model with a direct link to the input choice and show that the objective of reducing GHG is also a strong incentive to increase recycling, and that green policies can be implemented with this goal.
These articles add a significant contribution regarding public intervention linked to recy-cling activities. However this kind of static analysis omits the dynamic aspects of resource stocks mentioned above. A further analysis is needed to examine the arbitration between environmental externalities and resource depletion. For instance, extending the Acuff and Kaffine (2013) model (initially being an extension of the Palmer and Walls (1997) model) to a dynamic system.
An example of this can be found in Huhtala (1999). This is one of the few to analyze the optimal use of an exhaustible resource while considering issues of waste accumulation, resource depletion, and pollutant emissions at the same time. She describes the best arbi-tration of labor between recycling and primary production, and designs a fitting tax-subsidy scheme to achieve it under a balanced budget. This work is complemented by different recent studies on resource economics, with for instance Pittel et al. (2010) who model a decentralized economy with a recycling activity and highlight the market failure resulting from the absence of a market for waste, despite their economical value. They provide an optimum by setting up a market for waste and subsidizing recycling activities.
This dynamic approach is also the perspective of Di Vita (2001) and Di Vita (2007) who assess the possibility of an economic and welfare growth under a material constraint, thanks to investments in recycling. Sorensen (2017) also considers a recycling technology in a Ram-sey model that alleviates externalities due to resource extraction and consumption. These articles share the use of optimal control theory, but propose different models to represent a circular economy. Additionally, Di Vita (2001) and Di Vita (2007) propose models that do not respect a material balance in the economy in contrast to the physical reality of the use of secondary materials. With these propositions, they arrive to the conclusion that recycling allows a stationary growth path. An alternative modeling approach is given by Boyce (2012) who chooses to specify a recycling stock separate from accumulated waste. He examines the dynamic of this stock when there is perfect substitution between virgin and recycled material and he describes economic trade-offs between the two material to manufacture a final good.
The results of all these studies are in part driven by the substitutability characteristics of the production function. Models often use perfect substitution for virgin and recycled uses (Boyce, 2012; Hollander and Lasserre, 1988; Hoogmartens et al., 2018). While being a strong hypothesis, it remains relevant in our case of metal recycling with efficient processes (Villalba et al., 2002, 2004). While metal recycling has been a motivated topic for a long time (Ayres, 1997; Sigman, 1995), more recent concerns connected to technical changes and the energy transition have begun to be included. The essential place in modern technological applications taken by some materials (such as rare earth or lithium) also raises the question of how to bare the storage costs inherent to the industry as they are not evenly allocated worldwide (Rosendahl and Rubiano, 2019; Ba et al., 2020). As such, one could consider in-use material as a stock of resource (Batteries Europe, 2020).


A basic optimal recycling model

Setup of the model

We consider an industry that is managing a natural resource stock from which a final con-sumption good can be produced. We set an exogenous time-limit T to the management program, corresponding to the horizon of exploitation of the resource, before a shut down of the mine (Lappi and Ollikainen, 2019).
The industry can produce a quantity q of final good from two different inputs: the virgin resource and a recycled material, of relative quantities v and r. We assume perfect substitution between these two inputs, involving that q(t) = v(t) + r(t) for any time t. We also pose that waste is a one-to-one co-product of the final consumption good. Thus, q(t) also denotes the instantaneous flow of waste, before any potential recycling process.2 Consuming q units of final good provides a gross surplus u(q) to the final user, where u(.)
follows the standard hypotheses of utility functions: of class C2, increasing (u0 > 0), concave (u00 < 0) and verifying the Inada conditions, i.e. limq→0+ u0(q) = +∞ and limq→∞ u0(q) = 0. To account for the previously stated hypothesis of perfect substitution in the production function, we assume the utility drawn from the consumption of a good made out of virgin material is the same as that taken from the consumption of a good made out of recycled material.

Table of contents :

1 Recycling under environmental, climate and resource constraints 
1.1 Introduction
1.2 Related literature
1.3 A basic optimal recycling model
1.3.1 Setup of the model
1.3.2 Central planner program and optimal conditions
1.3.3 Arbitration on resources use
1.3.4 Recovering waste
1.3.5 Dynamics of resource flows
1.4 Accounting for climate change impacts
1.4.1 Optimal program with greenhouse gas emissions
1.4.2 Relative scarcity of the stocks and budget
1.4.3 Arbitration on resources use
1.4.4 Dynamics of resource flows
1.5 Decentralization and policy implications
1.5.1 Equilibrium in the absence of a waste market
1.5.2 Existence of a waste market
1.6 Conclusion
1.A Appendix
1.A.1 Scrap value for waste
1.A.2 Decoupling emissions of the recycling branch
1.A.3 Limiting the capacity of the recycling sector
2 Sectoral, resource and carbon impacts of increased paper and cardboard recycling 
2.1 Introduction
2.1.1 Context and motivations
2.1.2 Related literature
2.2 Adding a paper recycling loop to a forest sector model
2.2.1 Modular structure of FFSM
2.2.2 Dynamics of pulp recycling
2.2.3 Calibration and simulations strategy
2.3 Impact of paper recycling on the carbon balance
2.3.1 Impacts on the pulp industry
2.3.2 Impacts on other forest products
2.3.3 Impacts on the forest resource
2.3.4 Global carbon impact on the forest sector
2.4 Conclusion
3 An assessment of the European regulation on battery recycling for electric vehicles 
3.1 Introduction
3.2 Proposal of the European Commission
3.3 Qualitative Insights
3.4 Quantitative Analysis: Methods
3.4.1 Model
3.4.2 Data
3.5 Quantitative Analysis: Results
3.5.1 Evolution of RMD Ratios and Effect of Demand Growth
3.5.2 Effect of the Battery Lifespan
3.5.3 Effect of Technological Change
3.5.4 Effect of Recycling Efficiencies
3.6 Conclusion and Policy Implications
4 Recycling in a sustainable framework 
4.1 Context and motivations
4.2 Recycling and sustainability
4.3 A maximin model of recycling
4.3.1 Setup of the model
4.3.2 Characterization of the maximin path
4.3.3 Hartwick rule and sustainability
4.4 Conclusion
General conclusion 
Transversal and policy considerations
An holistic approach of recycling
Can recycling be bad?
Substitution and complementarity
Recycling and circular economy as a goal?
Future work
Recycling and sustainability accounting
Oligopolistic market structures for critical raw materials
Substituting virgin and recycled resources


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