Optimal input substitution of a firm facing an environmental constraint

In this paper we consider the dynamic behavior of a firm subject to environmental regulation. As a social planner the government wants to reduce the level of pollution. To reach that aim it can, among others, set an upper limit on polluting emissions of the firm. The paper determines how this policy instrument influences the firm's decisions concerning investments, abatement efforts, and the choice whether to leave some capacity unused or not. The abatement process is modeled as input substitution rather than end-of-pipe. Using standard control theory in determining the firm's optimal dynamic investment decisions it turns out that it is always optimal to approach a long run optimal level of capital. In some cases, this equilibrium is reached within finite time, but usually it will be approached asymptotically. Different scenarios are considered, ranging from attractive clean input to unattractive clean input, and from a mild emission limit to a very tight one. It is shown that for large capital stocks and/or when marginal cash flow per unit of emissions is larger for the dirty input than for the clean input, it can be optimal to actually leave some production capacity unused. Also, since the convex installation costs suggest to spread investments over time, it can happen that investment in productive capital is positive although capacity remains unused.