Complexities due to sluggish expansion of backstop technologies

This paper considers an economy using a technology that adds to a stock of pollution. Examples that come to mind are SO₂-emissions from burning coal accumulating in the soil and CO₂-emissions from fossil-energy use which are retained in the atmosphere. The stock of pollutants is subject to natural decay, albeit not necessarily of the simple often assumed linear type. In addition, a clean or so-called backstop technology is available that requires costly investments but is characterized by low variable costs (e.g., solar energy or wind power). The costly investments imply a slow build-up of the capacity of the backstop. On the modelling side, this is an essential extension of most of the literature that considers the unrealistic case where a backstop is instantaneously available. The second extension the present paper makes is to consider not only the planning problem but also the competitive outcomes. One of the interesting results is that stable limit cycles may characterize the socially optimal long-run outcome as well as the competitive equilibrium. In a competitive equilibrium pollution-control policy is not necessarily optimal in the sense of corresponding with the social optimum. Although cycling can occur in a competitive equilibrium, just as in the social optimum, relaxation of the control increases the set of parameter values for which complex and unstable behavior arises.