Optimal growth under irreversible pollution: The Forster-Ramsey model

We study optimal growth in a Ramsey economy with irreversible pollution, where the natural absorption capacity is non-monotonic and non-concave a la Forster. In the absence of pollution control, the capital dynamics decouple from pollution, and we characterize a simple threshold on the maximal absorption capacity above which the optimal path is sustainable and below which an optimal regime of irreversible pollution sets in. We then introduce an optimal abatement pollution control to assess whether irreversible pollution ceases to be optimal. We derive a four-dimensional dynamical system for capital, consumption, pollution and the (shadow) cost of pollution, coupled with an algebraic rule for optimal abatement. First, we show that while optimal abatement does shift the irreversibility threshold, it may not rule out optimal irreversible pollution paths. Second, and more importantly, we show that embedding the Forster's pollution dynamics into a Ramsey growth model generates a novel and robust hybrid ecological-economic irreversibility condition that is invisible in pollution-only frameworks. Coupling ecosystem curvature with the social discount rate, it is structurally robust and preeminent over all feasibility conditions amenable to policy intervention, and defines the boundary between a world where sustainability is achievable and one where it is not.