Capital accumulation of a firm facing an emissions tax

In this paper we consider the dynamic behavior of a firm that is subject to environmental regulation. It is assumed that, in order to prevent firms from polluting the environment excessively, the government imposes an emissions tax. We determine how an emissions tax influences the firm's decisions concerning investments and abatement efforts. In the model we incorporate the realistic property that a given abatement expenditure leads to more pollution reduction when pollution is large. This property implies increasing returns to scale with respect to pollution reduction. It turns out that, together with the usual assumption of decreasing returns to scale with respect to production, this property leads to the occurrence of history-dependent equilibria in case the pollution tax rate is sufficiently large. It is possible to derive an explicit formula for the threshold tax rate above which these history-dependent equilibria can occur. We show that an investment grant by the government can influence the firm so as to approach the equilibrium with a higher capital stock. Finally, we compare our results with those of a related model where the firm faces a strict pollution standard rather than an emissions tax. Among other things, we show that growth is more suppressed under a tax than under a standard when the firm is small.