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Markov chain modeling of the global technological lifetime of copper


  • Eckelman, Matthew J.
  • Daigo, Ichiro


Markov chain modeling is applied to the global anthropogenic copper cycle for the year 2000. The lifetime of copper varies from product to product and region to region, as well as through time. Assumptions of average lifetimes are therefore subject to a high degree of uncertainty. A large state transition table is created that encompasses the life-cycle stages of copper (mining, smelting, refining, fabrication, use, waste management, scrap, and final disposal), five end-uses (buildings, transportation, consumer products, electrical equipment, and machinery) in eight world regions, including trade at every stage. The system requires closure by mass balance, so all possible routes of copper trade and recycling are considered. Transitions between each pair of states are calculated using previous material flow analysis data. The main result is that an atom of copper is used 1.9 times by human society before it enters final disposal. Scaling by the lifetime of copper in each life-cycle stage in each region gives a total average technological lifetime of copper of 60Â years. A sensitivity analysis is applied to the model in order to test the robustness of the results. Several scenarios are also considered: increasing the recycling rate in each region to 70%, applying European or North American in-use lifetimes to all regions, and increasing the share of the world copper cathode and scrap markets taken in by Asia to 50%. Several limitations of the Markov chain approach are discussed, as are the further research opportunities it affords.

Suggested Citation

  • Eckelman, Matthew J. & Daigo, Ichiro, 2008. "Markov chain modeling of the global technological lifetime of copper," Ecological Economics, Elsevier, vol. 67(2), pages 265-273, September.
  • Handle: RePEc:eee:ecolec:v:67:y:2008:i:2:p:265-273

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    References listed on IDEAS

    1. I Weksler & D Freeman & G Alperovich, 1986. "Estimation of interregional trade flows: a Markov chain approach," Environment and Planning A, Pion Ltd, London, vol. 18(1), pages 123-132, January.
    2. I Weksler & D Freeman & G Alperovich, 1986. "Estimation of Interregional Trade Flows: A Markov Chain Approach," Environment and Planning A, , vol. 18(1), pages 123-132, January.
    3. Pyke, David F. & Cohen, Morris A., 1994. "Multiproduct integrated production--distribution systems," European Journal of Operational Research, Elsevier, vol. 74(1), pages 18-49, April.
    4. Ignacio Guzman, Juan & Nishiyama, Takashi & Tilton, John E., 2005. "Trends in the intensity of copper use in Japan since 1960," Resources Policy, Elsevier, vol. 30(1), pages 21-27, March.
    5. Spatari, S. & Bertram, M. & Fuse, K. & Graedel, T. E. & Rechberger, H., 2002. "The contemporary European copper cycle: 1 year stocks and flows," Ecological Economics, Elsevier, vol. 42(1-2), pages 27-42, August.
    6. Spatari, S. & Bertram, M. & Gordon, Robert B. & Henderson, K. & Graedel, T.E., 2005. "Twentieth century copper stocks and flows in North America: A dynamic analysis," Ecological Economics, Elsevier, vol. 54(1), pages 37-51, July.
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    Cited by:

    1. Faye Duchin & Stephen H. Levine, 2010. "Embodied Resource Flows and Product Flows: Combining the Absorbing Markov Chain with the Input-Output Model," Rensselaer Working Papers in Economics 1002, Rensselaer Polytechnic Institute, Department of Economics.
    2. repec:eee:ecolec:v:150:y:2018:i:c:p:297-306 is not listed on IDEAS
    3. Jean-Yves Courtonne & Pierre-Yves Longaretti & Julien Alapetite & Denis Dupré, 2015. "Environmental pressures embodied in the French cereals supply chain," Working Papers hal-01150067, HAL.
    4. Taulo, J.L. & Sebitosi, A.B., 2016. "Material and energy flow analysis of the Malawian tea industry," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 1337-1350.
    5. Courtonne, Jean-Yves & Alapetite, Julien & Longaretti, Pierre-Yves & Dupré, Denis & Prados, Emmanuel, 2015. "Downscaling material flow analysis: The case of the cereal supply chain in France," Ecological Economics, Elsevier, vol. 118(C), pages 67-80.
    6. García Muñiz, Ana Salomé & Ramos Carvajal, Carmen, 2012. "Linkages, contagion and resilience: an input-output scope from the demand and supply side," MPRA Paper 59369, University Library of Munich, Germany.
    7. Ana Salome GARCIA MUÑIZ & Carmen RAMOS CARVAJAL, 2015. "Input-Output Linkages And Network Contagion In Greece:Demand And Supply View," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 15(2), pages 35-52.
    8. Jean-Yves Courtonne & Julien Alapetite & Pierre-Yves Longaretti & Denis Dupré & Emmanuel Prados, 2015. "Downscaling material flow analysis: the case of the cereals supply chain in France," Working Papers hal-01142357, HAL.


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