Annals of Operations Research

, Volume 222, Issue 1, pp 457–481 | Cite as

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

  • Elke MoserEmail author
  • Andrea Seidl
  • Gustav Feichtinger


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.


Multi-stage modeling Production-pollution trade-off Optimal control Pontryagin’s maximum principle History-dependence 



We thank Franz Wirl, Alexia Fürnkranz-Prskawetz, Dieter Grass, Richard Hartl, Anastasios Xepapadeas, Peter Kort and Michael Rauscher for discussion and remarks. Further on, we thank the editors and referees for their valuable comments. This research was supported by the Austrian Science Fund (FWF) under Grant P21410-G16.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Elke Moser
    • 1
    • 2
    Email author
  • Andrea Seidl
    • 1
    • 2
  • Gustav Feichtinger
    • 1
    • 2
  1. 1.Institute for Mathematical Methods in Economics (IWM)Vienna University of Technology (TU Wien)ViennaAustria
  2. 2.Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OEAW, WU)/VID/OEAWViennaAustria

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