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Journal ArticleDOI

A Model of Eco-Efficiency and Recycling

AbstractThis paper presents the model of an economy subject to the mass conservation principle. The economic system is related to the environment by a flow of virgin materials into the economy, and by the diffusion of waste into the environment. Ecoefficiency contributes to reducing material waste in all processes. Recycling can reduce the diffusion of waste by feeding it back into the economy. Human capital enhances productivity, eco-efficiency and the quality of all kinds of outputs. Recycling and human capital formation use productive factors and are rooted therefore, as all other activities, in the material basis of the economy. The paper studies an optimal material state of society.

Topics: Eco-efficiency (53%)

Summary (4 min read)

1. INTRODUCTION

  • The current anthropogenic pressure on the natural environment calls for effective control of the material dimensions of human activities in advanced industrial societies (van den Bergh 1996; Adriaanse et al.
  • Physical capital occupies natural spaces and determines the material scale of the economy.
  • This implies, that recycling is a two-stage process: sequestration comes first and recycling in the stricter sense follows, when materials are extracted, or ‘mined’ out of sequestered materials and transformed into inputs to final output.
  • Human capital can contribute to reduce material losses in the process of transformation of material inputs into useful outputs (Reijnders 1998; Schmidt-Bleek 1993, 1997; Weizsäcker et al. 1997).
  • Sections 4 and 5 investigate a simplified reference case and offers an analytical discussion of the solution.

2.1. Material stocks and flows

  • The relationship between the environment and the economy is described in this paper by focussing on two material stocks, and on the flows between them.
  • From (2) and (3): De (4) Dv (5) A constant capital stock requires: Kcy K (6) where y are materials embodied in final output, c is aggregate physical consumption, and KK is linear capital depreciation.
  • I assume that these operations deliver processed materials of the same quality as the output of the virgin materials sector, so that processed virgin materials and processed waste are perfect substitutes.
  • Consumption is a materials processing sector of a particular kind: it transforms one fraction of final output into waste and yields welfare as its specific immaterial output1.

2.2. Materials processing sectors

  • I consider three materials processing sectors: a) extraction and refining of virgin materials, b) sequestration and recycling of waste and c) production of final output2.
  • From the economic point of view, processes are described by production functions, which establish a relationship between material flows and productive factors.
  • Clearly, tons of physical capital make sense in materials balance equations, but they make less sense in economic equations, since a ton of capital mass may provide different productive services, depending on the ‘shape’ or ‘form’ given to capital-matter by historically accumulated engineering knowledge.
  • Measures the additional effort required for recycling as compared to virgin materials extraction.
  • With (12) to (14) it is implicitly assumed, that the production function is the same in all sectors.

2.3. Consumption

  • Like other material flows, consumption is also measured in tons.
  • The benefits of physical consumption are enhanced by higher quality.
  • Processed virgin materials and recycled materials can be indifferently used therefore as perfect substitutes in final output production.
  • This means, that consumption is well above the level of survival and that its main role consists of enhancing life enjoyment.
  • There is a lower bound to this kind of substitution however, since physical per capita consumption cannot decline below a minimum level of calories, necessary for survival.

2.4. Human capital

  • Knowledge begins to shape materials already at extraction and recycling level, when materials to be extracted and recycled are selected and shaped in such a way, as they can best serve their purpose further down in the production process.
  • Knowledge thus permeates all stages of the economic process, although its results are only measurable when output reaches its final destination as capital or consumption good.
  • Sculptured marble will “loose” however more matter in transformation than unsculptured one, and eco-efficiency will be lower as a consequence of an improved aesthetic quality of marble, so that eco-efficiency is negatively affected by quality.
  • Equation (21) implies that the only material requirement in the science sector is physical capital, and ignores therefore other types of material inputs (e.g.: paper, fuel, etc.).
  • This means, that with rising eco-efficiency factors are shifted from materials processing to final output.

2.6. Preferences

  • The state of the environment is a public good and affects all of the identical N individuals in the same way.
  • Physical capital affects welfare in two ways: a direct, and an indirect one.
  • The indirect effect has been extensively analysed in economic theory: capital enhances labour productivity and contributes in this way to output and consumption.
  • At this point, the difference between physical and human capital may be summarized as follows.

3.1. The problem

  • Maintenance and renewal of depreciated human capital require capital and labour.
  • Human capital is limited by the same environmental constraints limiting the quantity of physical capital and is endogenously determined therefore along with the other stocks.

3.2. First order conditions

  • Kz zU is the direct negative marginal effect on consumption, deriving from the burden of capital depreciation.
  • Similarly, (31) compares benefits and costs of a marginal increase in recycling.
  • The lack of a second member on the right hand side is due to the fact that recycling does not increase the pollution stock.
  • Equation (32) compares the 17 consumptive benefits deriving from a marginal increase in eco-efficiency to the negative effects of an induced marginal increase in physical capital.

4. REFERENCE CASE

  • Given the number of variables and the non-linearity of the system, finding a solution may become quite an intricate business.
  • In the next section I shall present a graphic discussion of a simplified reference case, which allows to study the basic structure of the model.
  • For the simplified reference case I shall make following assumptions: a) Non depreciating physical capital Non-depreciating physical capital implies: 0K (33) b) I shall model utility as a logarithmic function of qualified consumption, net of quadratic environmental damage from stocks: 22 2 1log DqKqzqU DKz (29’) where iq are weights of the arguments in the utility function.

5.1. Efficient locus of non-negative recycling in v / space

  • I shall call this point the origin of the solution locus.
  • Point Q represents the origin of the locus in the case where (51) holds.
  • This implies, that the locus is monotonically falling.
  • The reason for this is simple: at 0D marginal damage from pollution is zero and there is no incentive therefore to prevent some materials to diffuse into the environment.

5.2 The solution point as a function of the size of the population

  • Without the necessity of calculating derivatives, one can also see, that 0 d dv , and that the graph shifts downwards for rising values of N . 22.
  • If the population increases, the graph shifts downwards.
  • Eco-efficiency increases and virgin material inputs into the economic system are substituted by recycled materials.
  • Therefore, if (51) holds, there is for non-negative recycling a lower limit to the size of the population.
  • In the case where (51) does not hold, the origin of the efficient locus is on the vertical axis and the size of the population in the origin is zero.

5.3. Physical capital

  • The graph shows, that physical capital declines as the growth of the population shifts the solution point downwards along the efficient locus.
  • This is because physical capital is substituted by labour and human capital as the population increases.
  • If physical capital and virgin material inputs both decline, this means, that the state oft the environment improves.
  • It may seem strange that in the stationary state the quality of the environment is better with a larger size of the population.
  • This result follows 23 however from the assumption of good substitutability between consumption and environmental quality in the social welfare function.

5.4. Physical per capita consumption.

  • This equation identifies points in v / space for given values of physical per capita consumption.
  • Any point on the efficient locus is associated with one level of per capita consumption.
  • How this looks like, depends however on the value of the Cobb-Douglas parameter .

5.4.4. A “large” value of .

  • The graph of 0,3 vg (pink curve), and the graph of (64) (green curves for two different values of physical per capita consumption) are represented in Figure 8: Figure 8.
  • For this reason, the graph shifts downwards as per capita consumption declines, and this means that with increasing population physical per capita consumption declines.

5.4.5. A “small” value of .

  • The graph of (64) is a loop, and the relevant feature is that an increase in b will not shift the graph upwards, as in the “large” case, but rather contract the loop.
  • According to (71) therefore, the upper part shifts downwards, and the lower part shifts upwards (and the loop therefore contracts) 26 as b increases.
  • For increases in the size of the population beyond the tangency point, obviously physical per capita consumption declines again.
  • This can happen without disrupting the environment, because capital is substituted by labour and recycling is increased.
  • Finally however, declining marginal returns and a decline in per capita consumption must prevail.

5.5. Carrying capacity

  • The present model is built on the assumption that consumption quantity can be substituted by quality.
  • There are obvious lower limits to such a kind of substitution, since, once consumption per head is reduced to a minimum caloric level, a further substitution of quantity with quality is no longer possible.
  • For this reason, there is an upper bound to the size of the population, given by carrying capacity, and this means, that there is a point on the efficient locus, below which a growth of the population is no longer sustainable.

6. CONCLUSIONS AND SOME WARNINGS

  • The model discussed in the previous sections investigates a material stock-flow equilibrium, supporting a sustainable economy.
  • The constraints imposed by the environment upon the accumulation of physical and human capital are described in this paper by two basic assumptions.
  • Recycling reduces flows of waste materials to the environmental sink, but achieves this by expanding other types of stocks, such as sequestration and recycling capital.
  • If this is not the case, an economic stationary state may turn out to be environmentally disruptive in the long run, and therefore ecologically unsustainable.
  • A fossil system will be capable of producing a stationary state of some duration, if an adequate technology for carbon recovery from the atmosphere becomes available (Holloway 2001).

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Cogoy, Mario
Working Paper
A Model of Eco-Efficiency and Recycling
Economics Discussion Papers, No. 2009-9
Provided in Cooperation with:
Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic
Challenges
Suggested Citation: Cogoy, Mario (2009) : A Model of Eco-Efficiency and Recycling, Economics
Discussion Papers, No. 2009-9, Kiel Institute for the World Economy (IfW), Kiel
This Version is available at:
http://hdl.handle.net/10419/27490
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Discussion Paper
Nr. 2009-9 | January 13, 2009 | http://www.economics-ejournal.org/economics/discussionpapers/2009-9
A Model of Eco-Efficiency and Recycling
Mario Cogoy
University of Trieste, Italy
Abstract
This paper presents the model of an economy subject to the mass conservation
principle. The economic system is related to the environment by a flow of virgin
materials into the economy, and by the diffusion of waste into the environment. Eco-
efficiency contributes to reducing material waste in all processes. Recycling can reduce
the diffusion of waste by feeding it back into the economy. Human capital enhances
productivity, eco-efficiency and the quality of all kinds of outputs. Recycling and
human capital formation use productive factors and are rooted therefore, as all other
activities, in the material basis of the economy. The paper studies an optimal material
state of society.
JEL: D90, O30, O41, Q00
Keywords: Eco-Efficiency, Recycling, Materials Balances, Material Flows, Human
Capital
Correspondence:
Mario Cogoy, Department of Economics and Statistics - University of Trieste, Piazzale Europa
1 - 34127 - Trieste – Italy, email:
mario.cogoy@econ.units.it
© Author(s) 2009. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany

2
1. INTRODUCTION
The current anthropogenic pressure on the natural environment calls for effective
control of the material dimensions of human activities in advanced industrial societies
(van den Bergh 1996; Adriaanse et al. 1997; Fischer-Kowalski 1998; Fischer-Kowalski
and Hüttler 1998; Ayres 1999b; Bouman et al. 2000). Different possible technological
responses to the task of controlling anthropogenic material flows have been discussed in
the literature as e.g.: dematerialisation, eco-efficiency, recycling, industrial ecology and
industrial metabolism.
Although the analysis of physical constraints on economic activities (Ayres 1998,
1999a; Cleveland and Ruth 1997; Ruth 1993, 1999) is a much debated issue, the
development of models combining physical insights with specific tools of economic
analysis still remains a very fragmentary field of research, since existing economic-
physical models make very different assumptions and focus on very different aspects of
the complex interaction between economic and physical analysis.
Smith (1972) applies the law of mass conservation to recycling in a model without
physical capital. He develops economic conditions for complete or zero recycling. Van
den Bergh (1996) presents an experimental model, based on materials balances. Waste
can be emitted, recycled or stored. Environmental quality depends on the stocks of
renewables and on the stock of pollutants. Simulations are performed with exogenous
scenarios. Di Vita (1997) studies the effects of recycling of imported raw materials on
the balance of payments and on employment in an open economy. Huhtala (1999)
investigates recycling as an alternative to resource extraction. Recycling reduces
pollution, but labour is the only input and physical capital does not come into the
picture. Nakamura (1999) applies an input-output approach to the study of waste
recycling in a static setting without technical progress. Di Vita (2001) focuses on the
effects of recycling on the rate of growth. His model includes technical progress, which
is endogenously generated by research. Welfare is negatively affected by the dimension
of the waste stock, but not by the scale of economic activities. Hosoda (2001) applies
the corn-guano model of the post-Sraffian school (Bidard and Erreygers 2001) to an
analysis of recycling. The residuals of a first process are used as inputs to a second

3
process. In this way, waste is completely absorbed and unlimited growth is possible,
even after exhaustion of landfills. Eichner and Pethig (2001) present a labour-only
model based on mass conservation with recycling activities and waste treatment before
disposal. They investigate waste markets and market failures in the waste sector.
Highfill and Mc Asey (2001) study recycling as an alternative to landfilling in the
framework of a growing economy. Economic growth is exogenous and no
interrelationship between physical capital, recycling and technical progress is therefore
addressed. Eichner (2005) applies a labour-only partial equilibrium model to the
analysis of imperfectly competitive markets in the recycling sector. André and Cerdá
(2006) analyse the intertemporal shift in the proportion between recyclable and non-
recyclable production inputs in a dynamic economy, not constrained by the mass
conservation principle and without capital accumulation and technical progress. An
overview of applied materials flows models is given in Bouman et al. (2000).
The present paper attempts to study material flows in an economic model, constrained
by the mass conservation principle, and in which technology is determined by human
capital. The flows considered are the flows between the natural environment and the
economy and the material flows within the economy. The stocks are: the stock of
accumulated emissions and the stock of materials temporarily frozen within the
economy in the shape of physical capital. Physical capital occupies natural spaces and
determines the material scale of the economy. If a recycling sector exists, materials are
re-directed from the flow of waste back into the economy as a second kind of material
inputs, which is added to the flow of virgin materials, directly extracted from the
environment.
There is some ambiguity in the literature on the nature of this second kind of material
inputs (Converse 1997; Ayres 1999a). Can waste be recycled after diffusion into the
environment, or is a previous sequestration of waste before diffusion necessary for
recycling activities? If diffused waste is the source of recycling, the difference between
virgin materials and recycled materials disappears, since both would have to be
extracted from the environment. I shall adopt the view of a combined sequestration-
recycling activity, because I assume that capturing waste materials before dissipation is

4
economically more convenient than retrieving materials after dissipation. In this case,
virgin materials and recycled materials are different inputs, since the first originate in
nature, while the second originate from sequestration activities. This implies, that
recycling is a two-stage process: sequestration comes first and recycling in the stricter
sense follows, when materials are extracted, or ‘mined’ out of sequestered materials and
transformed into inputs to final output.
The material structure of the economy is determined by knowledge and technology, and
the level of society’s technological capabilities is measured in this paper by human
capital. I shall consider three channels through which human capital influences the
material basis of human activities.
First of all, human capital contributes to an increase in productivity. This role of human
capital has been extensively investigated in economic theory (Lucas 1988; Romer 1989)
and will also be considered here. Productivity gains imply however a rising throughput
of materials, which has to be accounted for, both backwards, as an increase in material
requirements, and also forwards, as a growing production of waste.
A second effect of knowledge is to contribute to a more efficient use of materials in the
economic process. Human capital can contribute to reduce material losses in the process
of transformation of material inputs into useful outputs (Reijnders 1998; Schmidt-Bleek
1993, 1997; Weizsäcker et al. 1997). In this way, human capital enhances eco-
efficiency and reduces the environmental impacts of economic activities.
A third effect is on consumption. Consumption is not only a material, but also a
cultural, aesthetic and social process and is therefore fundamentally influenced by the
general level of accumulated social knowledge (Cogoy 1999).
In this paper I shall study the optimal material state of the economy in stock-flow
equilibrium. This means, that the social planner chooses the optimal level of stocks,
human capital included. The optimal level of knowledge is not infinite, since human
capital requires a material infrastructure supporting its operations, and is therefore
constrained by environmental considerations, as are all physical stocks. For this reason,
the optimal level of knowledge is endogenous in this paper. The description of a

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"A Model of Eco-Efficiency and Recyc..." refers background in this paper

  • ...INTRODUCTION The current anthropogenic pressure on the natural environment calls for effective control of the material dimensions of human activities in advanced industrial societies (van den Bergh 1996; Adriaanse et al. 1997; Fischer-Kowalski 1998; Fischer-Kowalski and Hüttler 1998; Ayres 1999b; Bouman et al. 2000)....

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  • ...In other words,  measures materials efficiency both at plant level and also at the level of interconnected plants (industrial ecology and industrial metabolism, cf. Ayres 1989; Ayres and Simonis 1994; Ayres and Ayres 1996; Erkman 1997)....

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  • ...In other words, measures materials efficiency both at plant level and also at the level of interconnected plants (industrial ecology and industrial metabolism, cf. Ayres 1989; Ayres and Simonis 1994; Ayres and Ayres 1996; Erkman 1997)....

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