Skip to main content
SpringerLink
Log in

Axioms of a Polluting Technology: A Materials Balance Approach

  • Published:
Environmental and Resource Economics Aims and scope Submit manuscript

Abstract

This paper aims to present an economic model characterized by a set of axioms that are consistent with the laws of thermodynamics. Two new axioms—weak G-disposability (i.e., weak directional disposability) and output essentiality—are introduced to satisfy the materials balance principle and the entropy law, respectively. The axiomatic production model is compared to other well-known production models that account for the joint production of good and bad outputs to illustrate the advantages of the new modeling approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. See for example the discussion in Daly (1997) and Stiglitz (1997).

  2. The most common approaches are modelling pollutants as weakly disposable outputs (see Färe et al. 1989, 2005) or freely disposable inputs (see Baumol and Oates 1975; Pittman 1981; Barbera and McConnell 1990).

  3. Clearly, the first law of thermodynamics encompasses both material and energy balances. However, in line with the literature on polluting technologies (Coelli et al. 2007; Førsund 2009), I focus solely on materials in the paper.

  4. The current paper concerns one bad output (byproduct) only. The purpose is to simplify the analysis and making it more transparent. However, the analysis may be generalized to multiple bads by introducing a vector of bads along with a material flow coefficient matrix.

  5. The material flow coefficients may vary across producers. For example, there exist various qualities of coal which differ in terms of their sulfur content and therefore require non-uniform flow coefficients across producers. The current paper does not make any input quality assessments and does therefore not deal with this issue.

  6. See Førsund (2009) for a more detailed discussion on the dynamics of end-of-pipe abatement.

  7. See the Electric Power Annual (http://www.eia.gov/electricity/annual/) for information on emission factors and electricity data.

  8. \(\vec {D}_O \left( {x,y+\alpha \delta _y ,b-\alpha \delta _b ;\delta _y ,-\delta _b } \right) =\vec {D}_O \left( {x,y,b;\delta _y ,-\delta _b } \right) -\alpha ,\,\alpha \in \mathfrak {R}\)

  9. The (selected) direction vector for the directional output distance function, \(\delta \), may differ from the G-direction, \(g=\left( {g_x ,g_y ,g_b } \right) \), in which inputs and outputs are disposable according to the G-disposability axiom.

  10. Notice that the G-disposability axiom is here defined such that the bad output must be considered a freely disposable input in order for the free disposability of inputs and outputs axioms to satisfy axiom (xii); G-disposability. The reason is that the G-disposability axiom implies that increases in inputs and the bad outputs are possible for any vector of good outputs.

  11. Coelli et al. (2007, p.7) correctly state that when keeping the good output vector fixed, the uncontrolled emissions (Eq. 1) are minimized when the aggregate material content of the inputs are minimized. Formally, \(\inf \limits _x \left\{ {ux-vy:x\in L\left( y \right) } \right\} =\inf \limits _x \left\{ {ux:x\in L\left( y \right) } \right\} -vy\), where vy is a fixed discount due to recuperation. This discount does, however, not appear in Coelli et al.’s environmental efficiency measurement framework. Only when the material flow coefficients for outputs are zero, the uncontrolled emission minimization (that includes the discount) coincides with Coelli et al.’s material inflow minimization.

  12. This point is illustrated by Hampf’s (2014) and Färe et al.’s (2013) recent contributions on the environmental efficiency of U.S. power producers. These papers attempt to explicitly model end-of-pipe abatement using network technologies, but their analyses are restricted due to limited data availability.

References

  • Ayres RU, Kneese AV (1969) Production, consumption, and externalities. Am Econ Rev 59:282–297

    Google Scholar 

  • Barbera AJ, McConnell VD (1990) The impact of environmental regulations on industry productivity: direct and indirect effects. J Environ Econ Manag 18:50–65

    Article  Google Scholar 

  • Baumgärtner S (2004) The Inada conditions for material resource inputs reconsidered. Environ Resour Econ 29:307–322

    Article  Google Scholar 

  • Baumgärtner S, Dyckhoff H, Faber M et al (2001) The concept of joint production and ecological economics. Ecol Econ 36:365–372

    Article  Google Scholar 

  • Baumol WJ, Oates WE (1975) The theory of environmental policy: externalities, public outlays, and the quality of life. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Chambers RG (1988) Applied production analysis: a dual approach. Cambridge University Press, Cambridge

    Google Scholar 

  • Chambers RG, Chung YH, Färe R (1998) Profit, directional distance functions, and Nerlovian efficiency. J Optim Theory Appl 98:351–364

    Article  Google Scholar 

  • Chung YH (1996) Directional distance functions and undesirable outputs. Southern Illinois University, Carbondale

    Google Scholar 

  • Chung YH, Färe R, Grosskopf S (1997) Productivity and undesirable outputs: a directional distance function approach. J Environ Manag 51:229–240

    Article  Google Scholar 

  • Coelli T, Lauwers L, Van Huylenbroeck G (2007) Environmental efficiency measurement and the materials balance condition. J Product Anal 28:3–12

    Article  Google Scholar 

  • Daly HE (1997) Georgescu-Roegen versus Solow/Stiglitz. Ecol Econ 22:261–266

    Article  Google Scholar 

  • Ebert U, Welsch H (2007) Environmental emissions and production economics: implications of the materials balance. Am J Agric Econ 89:287–293

    Article  Google Scholar 

  • Frisch R (1965) Theory of production. Reidel, Dordrecht

    Book  Google Scholar 

  • Färe R, Grosskopf S (2003) Nonparametric productivity analysis with undesirable outputs: comment. Am J Agric Econ 85:1070–1074

    Article  Google Scholar 

  • Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency in production. Kluwer-Nijhoff Publishing, Boston

    Book  Google Scholar 

  • Färe R, Grosskopf S, Lovell CAK et al (1989) Multilateral productivity comparisons when some outputs are undesirable: a nonparametric approach. Rev Econ Stat 71:90–98

    Article  Google Scholar 

  • Färe R, Grosskopf S, Lovell CAK et al (1993) Derivation of shadow prices for undesirable outputs: a distance function approach. Rev Econ Stat 75:374–380

    Article  Google Scholar 

  • Färe R, Grosskopf S, Noh D-W et al (2005) Characteristics of a polluting technology: theory and practice. J Econom 126:469–492

    Article  Google Scholar 

  • Färe R, Grosskopf S, Pasurka CA (2007) Pollution abatement activities and traditional productivity. Ecol Econ 62:673–682

    Article  Google Scholar 

  • Färe R, Grosskopf S, Pasurka CA (2013) Joint production of good and bad outputs with a network application. In: Shogren JF (ed) Encyclopedia of energy, natural resources and environmental economics. Elsevier, San Diego

    Google Scholar 

  • Färe R, Grosskopf S, Pasurka CA et al (2012) Substitutability among undesirable outputs. Appl Econ 44:39–47

    Article  Google Scholar 

  • Førsund FR (2009) Good modelling of bad outputs: pollution and multiple-output production. Int Rev Environ Resour Econ 3:1–38

    Article  Google Scholar 

  • Hampf B (2014) Separating environmental efficiency into production and abatement efficiency: a nonparametric model with application to US power plants. J Product Anal 41:457–473

    Article  Google Scholar 

  • Hoang V-N, Coelli T (2011) Measurement of agricultural total factor productivity growth incorporating environmental factors: a nutrients balance approach. J Environ Econ Manag 62:462–474

    Article  Google Scholar 

  • Krysiak FC, Krysiak D (2003) Production, consumption, and general equilibrium with physical constraints. J Environ Econ Manag 46:513–538

    Article  Google Scholar 

  • Lauwers L (2009) Justifying the incorporation of the materials balance principle into frontier-based eco-efficiency models. Ecol Econ 68:1605–1614

    Article  Google Scholar 

  • Mekaroonreung M, Johnson AL (2012) Estimating the shadow prices of \(\text{ SO }_{2}\) and \(\text{ NO }_{{\rm x}}\) for U.S. coal power plants: a convex nonparametric least squares approach. Energy Econ 34:723–732

    Article  Google Scholar 

  • Murty S, Russell RR (2002) On modeling pollution-generating technologies. Mimeo, University of California, Riverside

    Google Scholar 

  • Pethig R (2003) The “material balance approach” to pollution: its origin, implications and acceptance. Discussion paper, University of Siegen

  • Pethig R (2006) Non-linear production, abatement, pollution and materials balance reconsidered. J Environ Econ Manag 51:185–204

    Article  Google Scholar 

  • Pittman RW (1981) Issue in pollution control: interplant cost differences and economies of scale. Land Econ 57:1–17

    Article  Google Scholar 

  • Roma A, Pirino D (2009) The extraction of natural resources: the role of thermodynamic efficiency. Ecol Econ 68:2594–2606

    Article  Google Scholar 

  • Ruth M (1995) Thermodynamic implications for natural resource extraction and technical change in U.S. copper mining. Environ Resour Econ 6:187–206

    Article  Google Scholar 

  • Rødseth KL (2011) Treatment of undesirable outputs in production analysis: desirable modeling strategies and applications. Dissertation, Norwegian University of Life Sciences

  • Rødseth KL (2013) Capturing the least costly way of reducing pollution: a shadow price approach. Ecol Econ 92:16–24

    Article  Google Scholar 

  • Rødseth KL, Romstad E (2014) Environmental regulations, producer responses, and secondary benefits: carbon dioxide reductions under the Acid Rain Program. Environ Resour Econ 59:111–135

    Article  Google Scholar 

  • Shadbegian RJ, Gray WB (2005) Pollution abatement expenditures and plant-level productivity: a production function approach. Ecol Econ 54:196–208

    Article  Google Scholar 

  • Shephard RW (1970) Proof of the law of diminishing returns. Z Nationalokonomie 30:7–34

    Article  Google Scholar 

  • Shephard RW, Färe R (1974) The law of diminishing returns. Z Nationalokonomie 34:69–90

    Article  Google Scholar 

  • Stiglitz JE (1997) Georgescu-Roegen versus Solow/Stiglitz. Ecol Econ 22:269–270

    Article  Google Scholar 

Download references

Acknowledgments

The author thanks Finn R. Førsund and two anonymous referees for their helpful comments. The usual disclaimer applies.

Author information

Authors and Affiliations

  1. Institute of Transport Economics-Norwegian Centre for Transport Research, Gaustadalléen 21, 0349, Oslo, Norway

    Kenneth Løvold Rødseth

Authors
  1. Kenneth Løvold Rødseth
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kenneth Løvold Rødseth.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rødseth, K.L. Axioms of a Polluting Technology: A Materials Balance Approach. Environ Resource Econ 67, 1–22 (2017). https://doi.org/10.1007/s10640-015-9974-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10640-015-9974-1

Keywords

JEL Classification

Search

Navigation