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History-dependence in production-pollution-trade-off models: a multi-stage approach

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  • Elke Moser

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  • Andrea Seidl

    ()

  • Gustav Feichtinger

    ()

Abstract

Multi-stage modeling provides powerful tools to study optimal switches between different technologies. In most of the related literature, however, it is assumed that the number of switches is a-priori fixed. In the present paper we allow for multiple optimally determined switches. Consequently, we are able to locate solution paths that not only lead to different long-run outcomes but also differ in the number of switches along these paths. We present a simple production-pollution model in which a representative firm wants to maximize the profit gained out of production which, however, causes harmful pollution as by-product. The firm has the choice between two different technologies, one which is efficient in production but pollutive, and another one which is less efficient but environmentally friendly. With this two stage-model we focus on the numerical investigation of the conditions determining when and how often it is optimal for the firm to switch between these different technologies. We show that for certain parameters even several switches can be optimal and that the height of the switching costs crucially influences the long-run outcome. In the course of these investigations, we discuss two different economic mechanisms related to the harm due to pollution which lead to the occurrence of multiple equilibria, history-dependence and so-called Skiba points. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Elke Moser & Andrea Seidl & Gustav Feichtinger, 2014. "History-dependence in production-pollution-trade-off models: a multi-stage approach," Annals of Operations Research, Springer, vol. 222(1), pages 457-481, November.
  • Handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:457-481:10.1007/s10479-013-1349-9
    DOI: 10.1007/s10479-013-1349-9
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    Cited by:

    1. Raouf Boucekkine & Carmen Camacho & Benteng Zou, 2020. "Optimal switching from competition to cooperation: a preliminary exploration," PSE Working Papers halshs-02434786, HAL.
    2. Fouad El Ouardighi & Hassan Benchekroun & Dieter Grass, 2016. "Self-regenerating environmental absorption efficiency and the $$\varvec{ soylent~green~scenario}$$ s o y l e n t g r e e n s c e n a r i o," Annals of Operations Research, Springer, vol. 238(1), pages 179-198, March.
    3. Seidl, Andrea & Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M., 2018. "Serious strategy for the makers of fun: Analyzing the option to switch from pay-to-play to free-to-play in a two-stage optimal control model with quadratic costs," European Journal of Operational Research, Elsevier, vol. 267(2), pages 700-715.
    4. Seidl, Andrea, 2019. "Zeno points in optimal control models with endogenous regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 353-368.
    5. Richard F. Hartl & Peter M. Kort & Andrea Seidl, 2020. "Decisions on pricing, capacity investment, and introduction timing of new product generations in a durable-good monopoly," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 497-519, June.
    6. Stefan Wrzaczek & Michael Kuhn & Ivan Frankovic, 2020. "Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1065-1082, March.
    7. Zhen Li & Hongming Zhu & Qingfeng Meng & Changzhi Wu & Jianguo Du, 2019. "Manufacturers’ Green Decision Evolution Based on Multi-Agent Modeling," Complexity, Hindawi, vol. 2019, pages 1-14, April.

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