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

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.