Exploring the optimality of cyclical emission rates

In this paper, one of the basic assumptions is that the environment provides two different kinds of services. First, the environment may serve as an input to the production of conventional goods. For example, the exploitation of an oil source from which one firm extracts the oil which in turn is used as a fossil fuel for an industry. In the worst case, the use of the environment for industrial purposes will negatively affect the environment, e.g. the water quality of a paper mill along a river. Nevertheless, the possibility to pollute, i.e., to save abatement costs, lowers production costs. Hence, firms and consumers evaluate this service positively. Second, the environment itself-clean air, natural creeks and rivers instead of paper mills, hydro power plants, etc.-provides amenities and thus a second service that is different, because enjoying this service does not degrade environmental quality. As it is intuitively clear, the environment provides consumptive and non-consumptive uses. In renewable resources means, the environmental stock may be harvested and used as an input for conventional goods� production but provides simultaneously a positive externality. The purpose of this paper is to study the dynamics of pollution and the possibility of cycles and instability, while the major findings of this paper are the following: First, taking the simplest pollution model with one state and one control variables and extending it into two state variables, equilibrium may change from the fixed point into a limit cycle equilibrium, i.e. the optimal emissions rate may be cyclical. Second, taking the conflicting case as a differential game we found again the conditions under which the richer limit cycle equilibrium takes place.